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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 ?