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here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . | how do you use a cumulative z-table to calculate the percentage between two numbers using their z-scores ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | what is a z-score used for ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . | in what videos does sal teach how to determine z-scores more rigorously ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . | why is the z table ( based on a normal distribution having mean 0 and sd 1 ) usable for any other normal distribution ( having different mean and different sd ) ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet ,... | what if its and interval , such as what is the probability of getting a score between two numbers ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | how do i find absolute value using z score ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . | what is the median , lower quartile and upper quartile of 74 ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . | how can there be two types of standard deviation ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . | hiw do i explain the relationship between z scores and standard deviation ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . | 1 ) if 80 % of students are to be promoted , what should be the marks for promotion ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | what is the purpose of calculating z-score ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . | how do you know what problems to draw or not to draw a bell curve ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . | how can i specify my bell curve equation so that the maximum and minimum are defined ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | let 's see . we have a mean of 81 . that 's our mean . | so we can indicate the mean with both that little upside down 'h ' symbol by 81 and a greek letter 'm ' ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | what if z-score value is way bigger than the values provided in the table ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | let 's say z=8 , how do you find its probability if 8 does not match with any value of z from the table ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | what if z-score value is way bigger than the values provided in the table ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | let 's say z=8 , how do you find its probability if 8 does not match with any value of z from the table ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . | what is a bell curve ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . | why do you divide by the standard deviation ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . | for a normal distribution with mean -11 and standard deviation 0.2 , what values leaves probability 0.291 in both tails ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . | a study of 55 white mice showed that their average was 3.2 ounces.the standard deviation of the population is 0.9 ounces.which of the following is the 90 % confidence interval for the mean weight per white mouse ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? | why is z-score so important ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . | approximately what percentage of the observations should have a value greater than 35 but less than 55 ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . | would you have to use a standard normal table ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . | if you are working with a z-score , like in the activity set `` z-scores 3 '' ; how do you decide when to subtract the z-score from 1 or just use the given value ? |
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand... | so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . | x value is greater than 108 , mean 100 , standard deviation 8 , in the population and sampling distribution excel worksheet , can anybody help to find it ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . | what is the difference between the `` market revolution '' and the `` industrial revolution '' ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? | did booms and busts not happen under mercantilism ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . | which revolution was more impactful in the united states : the american or market ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . | did americans view having bosses as a threat to democracy ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . | are there any other particularly bad economic `` busts '' worth noting ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most rec... | i am sure we are all familiar with the panic of 1819 , the great depression , and the recession of 2008 , but were there any other really bad ones ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? | can someone give me a short summary of what an `` entry-market system '' is ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people lit... | was the labor of men and women treated differently or were they treated equally ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and ... | had a similar system of employment under a boss for a designated wage existed somewhere else before this time period ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the amer... | did the british have better technology in 1820 's ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . | why were children allowed to work in factories ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . | how is the industrial revolution different from the market revolution , are they similar ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is t... | how would these people find satisfaction in their work when consigned to the ranks of permanent wage laborers ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and tex... | were younger children also working in the mills or factories ? |
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revo... | so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . | what is the difference between the `` market revolution '' and the `` industrial revolution '' ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | what 's the difference between a 'subset ' and a 'strict subset ' ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . | is a null set also a subset of itself ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . | when would you use sets in real life ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a ... | so , is n't every set a subset and a `` strict '' subset of the universal set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | if a set contains 2 ( as a example ) elements , what will be the number of sets of it 's proper subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | why ca n't we write that `` a '' is a strict subset of `` a '' ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | how can b be a subset of a if b does n't have all of the elements that are in a ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . | one very simple question , what does `` notion '' mean ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets . | what is the differents between subsets and supersets ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . | a set has 3 elements , how many subsets does it have ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | what is the difference between a subset and a proper subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | could a subset be partially `` contained '' and still be called a subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | for example , a = { 2,4,6 } b = { 1,2,3 } is b a subset of a ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | how to symbolize `` not a subset of '' ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | can we write that a is a subset of b ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . | so does the order of the elements in the sets matter while saying this is a subset of that , that is , etc.. example : a = { 1,3,2 } , b = { 1 , 2 , 3 } can we say that a is also a subset of b ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | is c a subset of b ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . | why is a null set a subset of every set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . | what is the uses of an empty set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets . | does a null set have any strict subsets ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . | why would someone want to use the superset notation in place of the subset notation ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | why would someone use a is a superset of b instead of just saying b is a subset of a ( other than just wanting to have the letters in alphabetical order ) ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | so if a `` strict '' subset only rules out `` the exact same set '' ... why would you ever need to make a notation for `` strict '' subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | does a `` non '' strict subset realy come up that often ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets . | do you have the proof for finding the total number of subsets of a finite set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | is b also a strict subset of c ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . | and what is the power set and how do we solve it ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a ... | is null set/void set a 'strict ' subset or a 'not strict ' subset or any other set say a= { 1,2 } ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . | should n't the numbers in set c be in numerical order ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . | can a null set be a strict subset of itself or is nothing in the set considered something ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . | do you have to have the curly brackets around each number were were you could say that { 2 } is a subset of a or can you just say 2 ( without curly brackets ) is a subset of a. i know without the curly brackets is just a regular member but was n't sure if we 're checking subsets only or can we check just members too ag... |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . | is an empty set a subset of any set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | why is it false to say a is a strict subset of itself ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so let me write this . this is b . b is a strict or proper subset . | how to solve this a= { x^2+y^2=16 } and b= { 9x^2 + 25y^2=225 } , then n ( a intersection b ) = ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a ... | so do all of the members of a subset have to be in the original set , or just some ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . | is census of human a finite set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a ... | what is the point of having a subset because if a set is equal to a different set , well would n't you write equal not subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? | i realized that does the `` c '' ( as in c_ ) have to face the superset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | how will you know when to you the normal subset and when to use the strict subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . | why sets are denoted by capital letters ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | if a set contains 2 ( as a example ) elements , what will be the number of sets of it 's proper subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a ... | is every subset of a set either a strict subset or a subset that contains every member of the original set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a ... | so ... .could be set `` a '' a superset of itself as well ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets . | so are all sets subsets of the universal set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | then whats the difference between a subset and a strict subset ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . | if a= [ 1,2 ] and b= [ 3,2,1 ] ; is it right to say that a is superset or `` equal '' to b ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , ... | if yes , how can the '' equal to '' sign be verified ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . | what are equal and equivalent sets ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . | if a= { 1,2,3,4 } and b = { 1,2,2,3,3,3,4,4 } then , can we say a and b are equal ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets . | also can we say b is equivalent to a if we say a is equal to b in the first case ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets . | what subsets do 47 belongs to ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets . | how does the formula for computing the number of subsets for a certain set work ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | example : a { 1 , 2 , 3 , 4 , } b { 1 , 2 } b is a subset of a , b is a strict subset of a , a is a super set of b. is there such a thing as a strict super set ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | why we can not write a is strict subset of a ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . | what if you have a = { 1 , 2 , 3 , { 6 , 7 } , 5 } do you say { 6 } is an element of a ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . | do the curly braces make any difference ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . | what if a is a subset of b ? |
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want... | this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . | whats the difference between a subset and a strict subset ? |
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