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stringclasses 5
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sequence | answer
class label 3
classes | negate_openai_prompt
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|---|---|---|---|
Let V be the set of all real polynomials p(x). Let transformations T, S be defined on V by T:p(x) -> xp(x) and S:p(x) -> p'(x) = d/dx p(x), and interpret (ST)(p(x)) as S(T(p(x))). Which of the following is true? | [
"ST = 0",
"ST = T",
"ST = TS",
"ST - TS is the identity map of V onto itself."
] | 3D
| {
"content": "Please negate the text by adding negation cues or by substituting the main nouns/verbs/adjectives with their antonyms. Only reply with the negated sentence.\nSentence: Let V be the set of all real polynomials p(x). Let transformations T, S be defined on V by T:p(x) -> xp(x) and S:p(x) -> p'(x) = d/dx p(x), and interpret (ST)(p(x)) as S(T(p(x))). Which of the following is true?",
"role": "user"
} |
A tank initially contains a salt solution of 3 grams of salt dissolved in 100 liters of water. A salt solution containing 0.02 grams of salt per liter of water is sprayed into the tank at a rate of 4 liters per minute. The sprayed solution is continually mixed with the salt solution in the tank, and the mixture flows out of the tank at a rate of 4 liters per minute. If the mixing is instantaneous, how many grams of salt are in the tank after 100 minutes have elapsed? | [
"2",
"2 - e^-2",
"2 + e^-2",
"2 + e^-4"
] | 3D
| {
"content": "Please negate the text by adding negation cues or by substituting the main nouns/verbs/adjectives with their antonyms. Only reply with the negated sentence.\nSentence: A tank initially contains a salt solution of 3 grams of salt dissolved in 100 liters of water. A salt solution containing 0.02 grams of salt per liter of water is sprayed into the tank at a rate of 4 liters per minute. The sprayed solution is continually mixed with the salt solution in the tank, and the mixture flows out of the tank at a rate of 4 liters per minute. If the mixing is instantaneous, how many grams of salt are in the tank after 100 minutes have elapsed?",
"role": "user"
} |
Let A be a real 2x2 matrix. Which of the following statements must be true?
I. All of the entries of A^2 are nonnegative.
II. The determinant of A^2 is nonnegative.
III. If A has two distinct eigenvalues, then A^2 has two distinct eigenvalues. | [
"I only",
"II only",
"III only",
"II and III only"
] | 1B
| {
"content": "Please negate the text by adding negation cues or by substituting the main nouns/verbs/adjectives with their antonyms. Only reply with the negated sentence.\nSentence: Let A be a real 2x2 matrix. Which of the following statements must be true?\r\nI. All of the entries of A^2 are nonnegative.\r\nII. The determinant of A^2 is nonnegative.\r\nIII. If A has two distinct eigenvalues, then A^2 has two distinct eigenvalues.",
"role": "user"
} |
Suppose that f(1 + x) = f(x) for all real x. If f is a polynomial and f(5) = 11, then f(15/2) | [
"-11",
"0",
"11",
"33/2"
] | 2C
| {
"content": "Please negate the text by adding negation cues or by substituting the main nouns/verbs/adjectives with their antonyms. Only reply with the negated sentence.\nSentence: Suppose that f(1 + x) = f(x) for all real x. If f is a polynomial and f(5) = 11, then f(15/2)",
"role": "user"
} |
Let A be the set of all ordered pairs of integers (m, n) such that 7m + 12n = 22. What is the greatest negative number in the set B = {m + n : (m, n) \in A}? | [
"-5",
"-4",
"-3",
"-2"
] | 1B
| {
"content": "Please negate the text by adding negation cues or by substituting the main nouns/verbs/adjectives with their antonyms. Only reply with the negated sentence.\nSentence: Let A be the set of all ordered pairs of integers (m, n) such that 7m + 12n = 22. What is the greatest negative number in the set B = {m + n : (m, n) \\in A}?",
"role": "user"
} |
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