rationale stringlengths 0 4.7k | target stringlengths 1 171 | source stringclasses 13
values | prompt stringlengths 16 2.02k |
|---|---|---|---|
We have no idea if the person is trying to get a better view, people climb trees for a number of reasons.
| I don't know | esnli | Context: A person in a red shirt is climbing a tree branch in a forrest.
Hypothesis: A person is climbing a tree to get a better view.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Viscosity is resistance of fluid to deformation. Water is not resistant to deformation. | No | strategyqa | Does water have viscosity? |
Count of people would be less if some are absent | Yes | feasibilityQA | There are 59 students in a class and some of them are absent today.
Q: Is it true that "There could be 49 total students present in the class today." |
A town square can have structures and buildings and so a man standing in a town square might not be standing outside.
| Unknown | esnli | Consider the staetement "A man holds multiple flags while standing in a town square.". Based on this statement, is "a man stands outside" a true statement? Yes/no/unknown |
Just because players in white jerseys tackle a player in a red jersey does not imply that the white jersey team is winning.
| Unknown | esnli | Context: The two football players in white jerseys and purple pants tackle the player in the red jersey.
Hypothesis: The white jersey team is winning.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
Construction workers and a group of construction workers are equivalent as they work on the light rail tracks meaning they must be repairing railroad tracks.
| True | esnli | Context: "Construction workers in safety vests work on the light rail tracks." Claim: "A group of construction workers repair railroad tracks"
Considering the context, is the claim true, false, or unknown? |
The man cannot be kicking a football and kicking up dust simultaneously. The man cannot kick a football and ride a four-wheeler simultaneously.
| No | esnli | Consider the statement "A man kicks up dust on as he rides a four-wheeler, with a crystal blue sky in the background.". Based on this "The man is kicking a football." a true statement? Yes, no, or I don't know? |
If someone's husband is talking to his ex girlfriend all the time, it would likely make the person feel jealous and unloved instead of appreciated. | No | FLUTE | Context: When my husband and I first got together he use to talk to his ex girlfriend all the time cause she was with one of his friends.
Hypothesis: I felt really appreciated when my husband used to talk to his ex girlfriend all the time because she was with one of his friends
Given this context, determine if the hyp... |
A greenhouse is used to protect plants by keeping them warm.
Many orchids are rewarding indoor plants.
A greenhouse is used to protect orchids. | [c] | qasc | what is a greenhouse used to protect?
[a] cellulose
[b] Species
[c] orchids
[d] the sun
[e] h2o
[f] organisms
[g] glass
[h] our planet |
A skateboarder doing a handstand on a board does not mean he is on a skateboard or that the skateboard is very limber.
| I don't know | esnli | Given the statement "A skateboarder doing some kind of handstand on the board.", is the statement "The skateboard is very limber." is true?
- Yes
- No
- I don't know |
$$\frac{5}{37}=0.\overline{135}$$, it is a decimal which repeats in cycles of $3$ digits. $2021\div 3=673$$R2$, so the $2021$$^{st}$ digit is $3$. | (b) | TAL-SCQ5K | The $2021^{}\text{st}$ digit to the right of the decimal point in the decimal expansion of $\dfrac{5}{37}$ is~\uline{~~~~~~~~~~}~.
(a) $$2$$
(b) $$3$$
(c) $$4$$
(d) $$5$$ |
Middle adulthood lasts from the mid-30s to the mid-60s. During this stage of life, many people raise a family and strive to attain career goals. They start showing physical signs of aging, such as wrinkles and gray hair. Typically, vision, strength and reaction time start declining. Diseases such as type 2 diabetes, ca... | Group a | ropes | Context: David works for the government as a statistician. He had to produce a report for the coming annual meeting. This year he is thinking about a report with some lifestyle suggestions for middle adulthood population. To make it easier to understand the needs of middle adulthood population he would compare it with ... |
If the choir is standing It can not be sitting, a choir facing a congregation would not play cards.
| No | esnli | Given the statement "A choir in festive red stand facing the congregation of a church with a high, cavernous, arching ceiling.", is the statement "A group of people play card games at a table." is true?
- Yes
- No
- I don't know |
Sentence 2 is a simplified version of sentence 1. Many people on bikes, if they are wearing helmets or not
| Yes | esnli | Context: There are many people wearing helmets riding on bikes.
Hypothesis: many people on bikes
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Peeling something into a basket can also be described from the objects perspective as its being placed into a basket.
| No | esnli | Context: Young man peeling lemon with a knife into a red basket.
Hypothesis: A lemon being placed into a red basket
Is the hypothesis incorrect? (Yes, no, or unknown)? |
If Johnny had half as much practice as he currently has as of 20 days ago, this means he has 20*2=40 days worth of practice currently.
Therefore, to have three times as much practice as he currently has, he'd need to practice for 40*3=120 days.
Since he's already practiced for 40 days, this means he needs to practice o... | 80 | gsm8k | Johnny has been playing guitar for a while now. He practices the same amount each day. As of 20 days ago he had half as much practice as he has currently. How many days will pass before Johnny has 3 times as much practice as he does currently? |
35 bones at the end - 10 received = 25 on Sunday.
Lassie ate half, so multiply by two to find the number of bones at the beginning which is 25 * 2 = 50 bones. | 50 | gsm8k | Lassie eats half of her bones on Saturday. On Sunday she received 10 more bones. She now has a total of 35 bones. How many bones did she start with before eating them on Saturday? |
Air escapes a beach ball due to a hole or compromise in the ball's material/structural integrity. | "air leaked out of the beach ball because it had a picture on it" | senmaking | One of the following sentences is nonsensical. Which one is it?
* "air leaked out of the beach ball because it had a picture on it"
* "air leaked out of the beach ball because it had a hole on it" |
The first 10 floors are 10*12=120 feet
There are a remaining 20-10=10 stories
They are each 12+3=15 feet
So those stories are 15*10=150 feet
So the total height is 120+150=270 feet | 270 | gsm8k | James builds a 20 story building. The first 10 stories are each 12 feet tall each. The remaining floors are each 3 feet taller. How tall is the building? |
The digestive system breaks food into nutrients for the body.
Tapeworms have no digestive system and consist primarily of a reproductive system.
Something that tapeworms do not have breaks food into nutrients for the body. | Something that tapeworms do not have | qasc | What breaks food into nutrients for the body?
Options:
- Fully cooking the oysters
- secretion of acids and bases
- Eating and drinking
- the most widely used biofuel
- the stage of citokinesis
- To conserve energy
- Something that tapeworms do not have
- hydration of their cells |
One cannot speak into a microphone with a variety of recording equipment in front of him while in the shower, as water damages the equipment.
| False | esnli | Context: "A man is speaking into a microphone with a variety of recording equipment in front of him." Claim: "A man singing in the shower."
Considering the context, is the claim true, false, or unknown? |
That the hairdresser wears a red dress no longer necessarily implies gender these days, as a man might wear one instead of a woman. The customer could be either a man or a woman.
| Unknown | esnli | Given the statement "A young hairdresser in a red dress does a customers hair.", what is the statement "a woman styles a man's hair" true?
- Yes
- No
- Unknown |
It is not known why the man in blue sports clothes is pushing a dumpster. One cannot assume that he is throwing trash out. He could be doing something else.
| I don't know | esnli | Context: Brightly colored plastic crates lay piled high in the alley behind a brick building, near a man in blue sports clothes pushing a green dumpster.
Hypothesis: A man throwing trash out.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
- If something is outside during the day then that something will receive sunlight
- Puddles of water are outside during the day
- Hence, puddles of water will receive sunlight
- Puddles of water will receive sunlight
- If something receives sunlight, it will increase in temperature
- Hence, the puddles of water will ... | The water evaporated during the day. | entailment_bank | Q: In the morning, students observed puddles of water all over the playground. What would best explain why the playground was dry in the afternoon?
Context:
- Evaporation means a substance changes from a liquid into a gas by increasing heat energy
- Temperature is a measure of heat energy
- If something is outside du... |
设标价为$$x$$，进价为$$a$$，由题意得$$0.8x-a=0.2a$$解得$$x=1.5a$$，按原价出售可获利$$\frac{1.5a-a}{a}=0.5$$． | c | TAL-SCQ5K | 某件商品，若按标价的八折出售，可获利$$20 \%$$，若按原价出售，则可获利（ ~）
Options:
a. $$25 \%$$
b. $$40 \%$$
c. $$50 \%$$
d. $$66.7 \%$$ |
The longer sides are 2 in number so their total length of 2*28cm = 56cm
The rest of the length making up the short sides is 100-56 = 44 cm
There are two equal short sides so each one is 44/2 = 22cm | 22 | gsm8k | Bailey is making a rectangle out of a 100cm length of rope he has. If the longer sides of the rectangle were 28cm long, what is the length of each of the shorter sides? |
The two men are sitting and conversating rephrasing two men wearing sunglasses, one wearing a cowboy hat
| True | esnli | Context: "Two men wearing sunglasses, one wearing a cowboy hat and both in blue shirts, sit and talk." Claim: "The two men are sitting and conversating."
Considering the context, is the claim true, false, or unknown? |
We can call the three integers in this problem $a,$ $b,$ and $c$. Then we have \begin{align*}
a &\equiv 10\pmod{24}, \\
b &\equiv 4\pmod{24}, \\
c &\equiv 12\pmod{24}.
\end{align*}Adding these congruences, we have \begin{align*}
a+b+c &\equiv 10+4+12 \\
&= 26\pmod{24}.
\end{align*}Therefore, $a+b+c$ has the same remain... | $2$ | competition-math | When three positive integers are divided by $24$, the remainders are $10,$ $4,$ and $12,$ respectively.
When the sum of the three integers is divided by $24$, what is the remainder? |
Just because the lady asks the dog to give her the ball doesn't imply woman plays catch with her dog.
| Unknown | esnli | Context: The lady ask the dog to give her the ball on their beach walk.
Hypothesis: A woman plays catch with her dog.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
The brown dog is on a leash and appears to be playing with the white and brown colored dog does not imply that they were of the same breed.
| I don't know | esnli | Given the statement "The brown dog is on a leash and appears to be playing with the white and brown colored dog.", is the statement "The two dogs were of the same breed." is true?
- Yes
- No
- I don't know |
Frisbee is a game that involves throwing and catching a disc and the fact that the dog leaps over to catch the disc implies it is playing frisbee.
| Yes | esnli | Consider the statement "A dog leaps over a man to catch a disc.". Based on this "A dog plays Frisbee." a true statement? Yes, no, or I don't know? |
Just because two people performing in front of a crowd on a set of steps while wearing foil suits does not mean they are wearing foil suits perform a play on stange.
| Unknown | esnli | Consider the staetement "Two people performing in front of a crowd on a set of steps while wearing foil suits.". Based on this statement, is "Two people wearing foil suits perform a play on stange as the crowd looks on." a true statement? Yes/no/unknown |
Three men, two with shirts, one without working on the roof of a house does not imply that they are taring a roof.
| I don't know | esnli | Given the statement "Three men, two with shirts, one without working on the roof of a house.", is the statement "Three men are taring a roof." is true?
- Yes
- No
- I don't know |
Humans can jump to a limited distance. | No | feasibilityQA | Calvin was running and he came across a small ditch and he decided to jump
Q: Is it true that "He will land in another city." |
More minutes of workout is directly proportional to more calories burnt. | Yes | feasibilityQA | Richard worksout along with his friend. He burns less calories as compared to his friend. 80 is the number of minutes for which he works out.
Q: Is it true that "79 minutes could be the duration for which his friend worked out." |
Just because a baseball player is on the ground doesn't mean it's because he just slid into home plate.
| I don't know | esnli | Context: One baseball player is on the ground with his mouth open while another jumps above him.
Hypothesis: A baseball player on the ground has just slid into home plate.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
A backpacker standing on a trail surrounded by tall trees doesn't imply that the backpacker's backpack is large and tan.
| Unknown | esnli | Consider the staetement "A backpacker standing on a trail surrounded by tall trees.". Based on this statement, is "The backpacker's backpack is large and tan." a true statement? Yes/no/unknown |
In the U.S., the majority of electricity is produced by burning coal or other fossil fuels. This causes air pollution, acid rain, and global warming. Fossil fuels are also limited and may eventually run out. Like fossil fuels, radioactive elements are limited. In fact, they are relatively rare, so they could run out so... | Iran | ropes | Context:
Iran an Iraq are 2 neighbors. Iraq produces its electricity by burning fossil fuels, while Iran uses nuclear fission as its energy source.
Q: Which country causes less air pollution? |
The farmer has 51+5 = 56 cows in its herd.
The farmer sells 56/4 = 14 cows of the herd.
The farmer now has 56-14 = 42 cows. | 42 | gsm8k | A farmer has 51 cows. The farmer adds five new cows to its herd and then sells a quarter of the herd. How many cows does the farmer have left? |
A Library is a quiet place to study. | "we held a party in the library last week" | senmaking | Pick which sentence is not logical.
- "we held a party at katie's house last week"
- "we held a party in the library last week" |
There is no indication that the man standing in front of a crowd of people would be waiting for a hotdog.
| I don't know | esnli | Consider the statement "A man with a yellow and green shirt is standing in front of a crowd of people.". Based on this "The man is waiting for his hotdog." a true statement? Yes, no, or I don't know? |
Mating is generally preceded by courtship.
Moose courtship begins in autumn.
Moose mating happens around autumn. | 1 | qasc | Moose what happens around autumn
Options:
1: mating
2: Winter
3: migrate
4: complex
5: howling
6: interact
7: movement
8: moves |
Faulting of rock in earth 's crust causes earthquakes.
Earthquakes can cause a tsunami.
Faulting of rock in the earth's crust can cause a tsunami. | (E) | qasc | What can be caused by a faulting of the earth's crust?
(A) a hurricane
(B) a hail storm
(C) waves
(D) graptolites
(E) a tsunami
(F) loose soil
(G) river
(H) erosion |
Occupants can not exceed the capcity of a hotel | Yes | feasibilityQA | The hotel Grand can accommodate 191 customers at once.
Question: Is the following statement plausible?
On Monday, 146 customers could be residing in the hotel. |
At regular price, the polo shirts are 2 x $50 = $100.
At 40% off, he gets a discount of , $100 x 40% = $40.
With this discount, the polo shirts cost $100 - $40 = $60. | 60 | gsm8k | Zane purchases 2 polo shirts from the 40% off rack at the men’s store. The polo shirts are $50 each at the regular price. How much did he pay for the shirts? |
Electric bill of two houses combined is more than that of an individual house | Yes | feasibilityQA | Jace pays electric bill for his house and his brother's house every month. His bill for this month was 549 dollars.
Q: Is it true that "The combined electric bill could be 649 dollars." |
An artist is someone creative, and a young boy is another person; a comical sketch is something funny.
| No | esnli | Consider the statement "An artists is drawing a comical sketch of a young boy.". Is the statement "Someone creative is making something funny about another person." false? Yes/no/unknown |
Newt Gingrich was born Newton Leroy Gingrich and goes by the nickname Newt. A newt is a type of Amphibian with smooth, sticky skin.. Reptiles have dry and hard skin. | No | strategyqa | Is Newt Gingrich's nickname a type of Reptile? |
A noodle is a type of pasta that is soft, so saying that her backbone was like a noodle means it was flexible, not rigid | False | FLUTE | Context: "This morning, she tried to get out of bed but the blankets and pillows were in the way; she could only flounder gracelessly up to her elbows, and her backbone felt rigid."
Hypothesis: This morning, however, blankets and pillows thwarted her; she could only flounder gracelessly up to her elbows, her backbone l... |
Cholesterol can't dissolve in the blood. It has to be transported to and from the cells by carriers called lipoproteins. Low-density lipoprotein, or LDL, is known as "bad" cholesterol. High-density lipoprotein (HDL) is known as good cholesterol. When too much LDL cholesterol circulates in the blood, it can slowly build... | Patient b | ropes | John is a doctor with the local hospital. Earlier today, he was seeing two patients, patient A and patient B. John found out that patient A had more LDL, but patient B had more HDL. He now needs to determine correct treatment for them.
Based on the above, answer the following question:
Which patient would less likely r... |
A man with a dog and a woman carrying something blue in a clear plastic bag, standing on a city street does not imply they are husband and wife
| I don't know | esnli | Context: A man with a dog and a woman carrying something blue in a clear plastic bag, standing on a city street.
Hypothesis: The husband and wife are walking the dog and returning something to a store.
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Standing beside a ladder, wagon, and bales of hay does not necessarily imply that people are farming.
| Unknown | esnli | Context: "Three men and two women are standing besides a ladder, a wagon, and bales of hay." Claim: "they are farming"
Considering the context, is the claim true, false, or unknown? |
Talking on a cellphone near a building does not imply that a man is discussing a new business idea.
| Unknown | esnli | Context: An older man stands by a building talking on his cellphone.
Hypothesis: A man discusses a new business idea on his cellphone.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
The men cannot be jogging if they are skydiving. Skydiving takes place in the air, jogging takes place on the ground.
| No | esnli | Context: Two men, one in a yellow jersey, the other red, jogging on a fall day.
Hypothesis: two men are skydiving
Given this context, is the hypothesis true (Yes/No/I don't know)? |
Almost all earthquakes occur at plate boundaries. All types of plate boundaries have earthquakes. Convection within the Earth causes the plates to move. As the plates move, stresses build. When the stresses build too much, the rocks break. The break releases the energy that was stored in the rocks. The sudden release o... | Red | ropes | Consider the following text:
Two sister cities were both situated on plate boundaries, close to volcanoes, on different continents. Red city was 10 miles from a volcano, while Tree city was 60 miles away. Red city experienced many earthquakes, Tree city few and far between.
Which city experienced more stress build up ... |
A man is clearing a pump in front of the drake hotel, then he must be in front of the hotel, they are both in the front of the drake hotel
| True | esnli | Context: "A man in a green machine is cleaning a pump in front of the Drake hotel." Claim: "A man is in front of the Drake hotel."
Considering the context, is the claim true, false, or unknown? |
To pull strings is to use power or influence to get what one wants, which is what he would be doing if he could get a monaco transfer. | Yes | FLUTE | Given the statement "You think he'd still be in Belgium if he could use his power or influence to get a monaco transfer?", what is the statement "You think he'd still be in belgium if he could pull strings for a monaco transfer?" true?
- Yes
- No
- Unknown |
A basketball court consists of a basketball net and shooting a basketball is synonym of tossing a basketball.
| No | esnli | Given the statement "A little boy shooting a basketball on a basketball court.", is the statement "A young boy tosses a basketball toward a basketball net." wrong?
- Yes
- No
- Unknown |
The first sentence doesn't specify why the kids are in front of the computer, that they are on a video chat and talking with their dad.
| Unknown | esnli | Context: "Two kids smiling in front of the computer"
Hypothesis: Two kids are smiling on video chat as they talk with their dad.
Based on the context, is the hypothesis true, false, or unknown? |
A stunt driver is attempting to drive with only one side his four-wheeler touching the ground doesn't imply he is performing a stunt.
| Unknown | esnli | Context: A stunt driver is attempting to drive with only one side his four-wheeler touching the ground.
Hypothesis: The stunt driver is trying to perform a stunt in only one take.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
You cannot find a lemur by choosing one. | [b] | senmaking | Choose the sentence that goes against common sense.
[a] "you are trying to find a lemur in lemur land"
[b] "you are trying to choose a lemur in lemur land" |
A sunset is generally considered to be a beautiful scene, and an icy hell is a violent place, so saying it was like a cold sunset filled with the furious motion of an icy hell implies that it was both beautiful and violent | Yes | FLUTE | Consider the statement "It was neither beautiful nor violent". Is the statement "It was like a cold sunset filled with the furious motion of an icy hell." false? Yes/no/unknown |
Dirty trash bin is used only to put waste, it will be disgusting to cook. | 1 | senmaking | Which of the following sentences is nonsensical?
1: "she uses the trash bin to cook"
2: "she uses the pot to cook" |
The beauty of Tahiti is often mentioned and therefore it is likely to make someone envious if their best friend gets to go there and they don't. | No | FLUTE | Context: My best friend is going to Tahiti with his family!
Hypothesis: Tahiti is the most beautiful place on Earth and it doesn't make me envious of my best friend who gets to go there unlike me
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Earth orbits around the Sun in 365 days. Napoleonic Wars lasted 12 years, 5 months and 4 weeks. | Yes | strategyqa | Did earth complete at least one orbit around the sun during the Napoleonic Wars? |
Assuming the brick building is the theater, there can either be no people, or some people outside of the building.
| No | esnli | Context: Four people walking along the side of a brick building.
Hypothesis: There are no people outside the theater.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
The balls used in squash are small rubber balls that can differ in terms of diameter, weight and softness. These features determine the speed and bouncing amplitude of the ball, with softer balls being generally slower than the harder balls. The temperature of the ball also affects the amount of bounce: the warmer the ... | Thomas | ropes | Consider the following text:
Thomas and Joseph, two experienced squash players, are having a disagreement about which types of squash balls they should use in their match. Both have different preferences for the type of ball used. Joseph prefers a ball that bounces less and travels more slowly. Thomas, on the other han... |
The fact they are trying to score does not mean they are not doing great; scoring goals is the goal in a hockey game.
| Unknown | esnli | Context: "A hockey team is trying to score a goal." Claim: "The hockey team is not doing so great."
Considering the context, is the claim true, false, or unknown? |
A large woman in a tan shirt and brown pants uses a microphone does not necessary that they watched by a group
| I don't know | esnli | Context: A large woman in a tan shirt and brown pants uses a microphone.
Hypothesis: watched by a group
Given this context, is the hypothesis true (Yes/No/I don't know)? |
A beach can be next to a sea or some other body of water and not necessarily an ocean. Kids can go to the beach even if they have no intention of going swimming.
| Unknown | esnli | Context: Two kids running down a sand dune to the beach.
Hypothesis: Two kids head towards the ocean to go swimming.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
Just because event staff are preparing doesn't mean they are preparing for event that takes place in two weeks.
| I don't know | esnli | Consider the statement "A group of Event Staff move in and around two stalls covered in target logos in front of a building with arched windows.". Based on this "The staff is preparing for an event that will take place in two weeks" a true statement? Yes, no, or I don't know? |
Just because someone is holding a pair of flip flops does not mean he is now barefoot. He might be wearing a second set of shoes while carrying the flip flops.
| Unknown | esnli | Context: Little boy in orange shirt, holding flip-flops has his hand on his head.
Hypothesis: The boy is now barefoot because he has flip-flops on his head.
Is the hypothesis incorrect? (Yes, no, or unknown)? |
On the second row, he used 9 - 2 = 7 blocks.
On the third row, he used 7 - 2 = 5 blocks.
On the fourth row, he used 5 - 2 = 3 blocks.
On the fifth row, he used 3 - 2 = 1 block.
Therefore, he used a total of 9 + 7 + 5 + 3 + 1 = 25 blocks. | 25 | gsm8k | A child is making a 5-level pyramid by stacking some blocks. In the first row, he has 9 blocks. For the next rows, he has 2 less than the blocks he has from its bottom row. How many blocks did he use in all? |
The largest common factor of $9x^2$ and $3x$ is $3x$. We factor $3x$ out of each term to get\begin{align*}
9x^2+3x &= 3x\cdot 3x + 3x \cdot 1\\
&= 3x(3x+1).
\end{align*} | $3x(3x+1)$ | competition-math | Completely factor the following expression: $9x^2+3x$. |
Pointing and gesturing are two different motions. There is nothing that leads me to know that the woman is either gesturing or pointing to today's newspaper in the stand - she could be pointing towards anything.
| Unknown | esnli | Given the statement "Woman in striped sweater uses blue umbrella to gesture towards something.", what is the statement "A woman is pointing to today's newspaper in the stand with her umbrella." true?
- Yes
- No
- Unknown |
A young child is filling a bucket of water from a faucet. while at the same time wouldnt be A little kid is putting water in a pail.
| Yes | esnli | Consider the staetement "A young child is filling a bucket of water from a faucet.". Based on this statement, is "A little kid is putting water in a pail." a true statement? Yes/no/unknown |
由题中给出的四个结论，可知本题需根据解方程的情况作出选择，于是考虑在方程 $$\overline{Z}-\lambda Z=W$$ 的两端同取共轭，得 $$Z-\overline{\lambda Z}=\overline{W}$$， 以$$\lambda $$乘两端，得 $$\lambda Z-{{\left\textbar{} \lambda \right\textbar}^{2}}\overline{Z}=\lambda \overline{W}$$ 与原方程两端分别相加，得 $$\overline{Z}(1-{{\left\textbar{} \lambda \right\textbar}^{2}})=\lamb... | 只有（1）和（2）是正确的 | TAL-SCQ5K | 设$$Z,W,\lambda $$为复数$$\lambda
e 1$$，关于$$Z$$的方程$$\overline{Z}-\lambda Z=W$$有下面四个结论： （1）．$$Z=\frac{\overline{ \lambda }W=\overline{W}}{1-\textbar\lambda{{\textbar}^{2}}}$$是这个方程的解； （2）这个方程只有一个解； （3）这个方程有两个解； （4）这个方程有无穷多解．则．
Options:
- 只有（1）和（2）是正确的
- 只有（1）和（3）是正确的
- 只有（1）和（4）是正确的
- 以上$$A$$、$$B$$、$$C$$都不正确 |
A young female student performing a downward kick to break a board held by her Karate instructor, while at the same moment couldn't be a young woman that demonstrates Karate.
| Yes | esnli | Given the statement "A young female student performing a downward kick to break a board held by her Karate instructor.", what is the statement "A young woman demonstrates Karate." true?
- Yes
- No
- Unknown |
Adult tunicates are barrel-shaped.
Tunicates, or sea squirts, are marine organisms covered with a gelatinous tunic.
Adult sea squirts are barrel-shaped. | F | qasc | what adults are barrel-shaped?
Options:
A) offspring
B) fertile
C) barnacles
D) Length
E) insects
F) sea squirts
G) humans
H) beer |
Sentence 1: People walking down a busy street in the middle east. Sentence 2: people may be watching cars
| Unknown | esnli | Context: "People walking down a busy street in the middle east."
Hypothesis: people may be watching cars
Based on the context, is the hypothesis true, false, or unknown? |
Some precipitation that falls on land may soak into the ground, becoming groundwater.
Rain is also known as precipitation.
Rain that falls on land may soak into the ground and become groundwater. | groundwater | qasc | What is rain that absorbs into the earth called?
* aqueous solution
* heat energy
* soilwater
* groundwater
* peachleaf willow
* mud
* puddle
* water vapor |
The human is the man in the military fatigues and another human is another man who is lying on the ground in front of a row of parked cars
| No | esnli | Consider the statement "A man in military fatigues is assisting another man who is lying on the ground in front of a row of parked cars.". Is the statement "A human assisting another" false? Yes/no/unknown |
If an object reflects light toward the eye then that object can be seen.
Objects are seen by virtue of scattered light.
By virtue of scattered light objects reflects light toward the eye. | b | qasc | By virtue of what can objects reflects light toward the eye?
a. sunlight
b. scattered light
c. bright light
d. destroyed light
e. sensory neurons
f. Electrical energy
g. flow of electrons
h. speckled light |
People walk through parks, going under would mean you somehow go underground. | "i walked under the park." | senmaking | Of the following two sentences, which one is against common sense?
Options:
"i walked across the park."
"i walked under the park." |
If people are wearing jerseys and kicking a soccer ball it is reasonable to assume they are playing soccer.
| Yes | esnli | Context: A boy in a blue jersey kicks a soccer ball into the head of a boy in an orange jersey.
Hypothesis: Someone is playing soccer.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
T = 60/36 * 18/5 = 6 sec | [d] | aqua | n what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
[a] 2
[b] 7
[c] 8
[d] 6
[e] 9 |
If a group of individuals are on the lawn then that means nobody can not be there. Summer means it is not winter.
| No | esnli | Context: A varied group of individuals sit on a lawn in the summer.
Hypothesis: Nobody on the lawn in winter.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
A quarter of the number is 27-15=12.
The number is 12*4=48. | 48 | gsm8k | Fifteen more than a quarter of a number is 27. What is the number? |
三角形内角和为$$180$$度，这个三角形最大的角为$$180\times \frac{4}{2+4+3}=80$$（度），为锐角三角形． | 2 | TAL-SCQ5K | 一个三角形的三个内角度数比为$$2:4:3$$，这个三角形是．
1: 钝角三角形
2: 锐角三角形
3: 直角三角形
4: 不能确定 |
you cannot play in the water and playing in the sand at the same time. The adults are either holding his hand or tanning
| No | esnli | Given the statement "A little boy playing in the water while its raining and an adult while an adult holds his hand", is the statement "The boy is playing in the sand while the two adults tan." is true?
- Yes
- No
- I don't know |
A garage is not alive and cannot be walked. | [2] | senmaking | Of the below sentences, which one does *not* make sense?
[1] "i walked my dog yesterday."
[2] "i walked my garage yesterday." |
Just because the road is being worked on at night, does not mean the purpose of working at night is to encounter less traffic.
| Unknown | esnli | Context: "Construction workers work on a road into the night." Claim: "Construction workers decided to work at night when there was less traffic."
Considering the context, is the claim true, false, or unknown? |
A girl tucked into bed is not one who sits. A girl in bed with a moon out is there to sleep; the room would not normally be full of people.
| No | esnli | Given the statement "A little redheaded girl sits in front as the tiny trail full of people approaches the tiny water tower.", what is the statement "A girl with red hair is tucked into her bed by the window with a full moon out." true?
- Yes
- No
- Unknown |
If a man and a woman do not know what a motorcycle is, then they would not be near motorcycle helmets.
| Yes | esnli | Consider the statement "A man and woman sitting on a ledge in a close embrace in front of two motorcycle helmets.". Is the statement "The man and woman do not know what a motorcycle is." false? Yes/no/unknown |
Acceleration is a measure of the change in velocity of a moving object. It measures the rate at which velocity changes. Velocity, in turn, is a measure of the speed and direction of motion, so a change in velocity may reflect a change in speed, a change in direction, or both. Both velocity and acceleration are vectors.... | Slower | ropes | Context: Angela is driving on a highway. She is stuck between two cars but needs to get to the off ramp and decides to speed up. She hits the gas making her car go faster so she can get ahead of the two cars she is stuck in between and makes it to the ramp in time.
Question: Given Angela decided decelerate instead woul... |
If the surfer is skilled, then he would be concentrating on surfing instead of drinking a sode when he is surfing.
| No | esnli | Consider the staetement "A skilled surfer grabbing the tip of his board while the rides a wave.". Based on this statement, is "A surfer is riding w ave while grabbing the tip of his board while drinking a sode." a true statement? Yes/no/unknown |
Several people cannot be considered family and television cannot be under an overhang on stone steps.
| False | esnli | Context: "Several people are sitting under an overhang on stone steps." Claim: "A amily eating dinner in front of the television."
Considering the context, is the claim true, false, or unknown? |
Just because A man in snow weather gear is laying in the snow in front of a door does not indicate that he is in snow gear lays in the snow pretending to be dead.
| Unknown | esnli | Given the statement "A man in snow weather gear is laying in the snow in front of a door.", is the statement "A man in snow gear lays in the snow pretending to be dead." wrong?
- Yes
- No
- Unknown |
An elderly gentleman playing a musical instrument on the sidewalk for money does not mean he is saving up for a new instrument
| Unknown | esnli | Context: An elderly gentleman playing a musical instrument on the sidewalk for money.
Hypothesis: The old man is saving up for a new instrument.
Given this context, determine if the hypothesis is true (Yes, no, or unknown)? |
A dog adorned with a ribbon must have a ribbon pinned to him while ribbons are displayed behind him means there are ribbons behind him.
| Yes | esnli | Consider the statement "A brown dog has a blue and white ribbon pinned to him, and teal and yellow ribbons behind him.". Based on this "A dog is adorned with a ribbon while ribbons are displayed behind him." a true statement? Yes, no, or I don't know? |
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