sample_id stringlengths 18 47 | sentence stringlengths 4 4.5k | prompt stringlengths 185 4.93k | correct_name stringlengths 1 819 | choices dict | answer stringclasses 4
values | positive_answer0 stringlengths 4 822 | negative_answer1 stringlengths 4 884 | negative_answer2 stringlengths 4 749 | negative_answer3 stringlengths 4 648 | task stringclasses 57
values | demonstrations stringlengths 4.01k 35.5k | concatenated_prompt stringlengths 4.36k 38.5k | retrieved_examples listlengths 16 16 | num_demonstrations int64 16 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mmlu-abstract-algebra.val.81 | Statement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | Every nonzero free abelian group has an infinite number of bases. Statement 2 | Every free abelian group of rank at least 2 has an infinite number of bases.\nA) True, False\nB) True, True\nC) False, False\nD) False, True\nPrint only a single choice... | False, True | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"True, False",
"True, True",
"False, False",
"False, True"
]
} | D | D. False, True | A. True, False | B. True, True | C. False, False | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | There exists a free abelian group of every positive integer rank. Statement 2 | A finitely generated abelian group is free abelian if its Betti number equals the number of elements in some generating set.\nA) False, False\nB) True, True\n... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | There exists a free abelian group of every positive integer rank. Statement 2 | A finitely generated abelian group is free abelia... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | There exists a free abelian group of every positive integer rank. Statement 2 | A finitely generated abelian group is free abelian if its Betti number equals the number of elements in som... | 16 |
mmlu-abstract-algebra.val.82 | Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.\nA) True, False\nB) False, False\nC) True, True\nD) False, True\nPrint ... | True, True | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"True, False",
"False, False",
"True, True",
"False, True"
]
} | C | C. True, True | A. True, False | B. False, False | D. False, True | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.\nA) False, False\nB) True, False\nC) True, True\nD) False, True\nPrint only a single choi... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah =... | [
{
"retrieved_answer": "A",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | If H is a subgroup of a group G and a belongs to G, then aH = Ha. Statement 2 | If H is normal of G and a belongs to G, then ah = ha for all h in H.\\nA) False, False\\nB) True, False\\nC... | 16 |
mmlu-abstract-algebra.val.83 | Statement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | If a group has an element of order 10, then it has elements of orders 1, 2, and 5. Statement 2 | If a group has an element of order 2 and an element of order 3, then it has an element of order 6.\nA) True, False\nB) True, True\nC) False, True\nD) F... | True, False | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"True, False",
"True, True",
"False, True",
"False, False"
]
} | A | A. True, False | B. True, True | C. False, True | D. False, False | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.\nA) False, False\nB) False, True\nC) True, False\nD) True, Tru... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | The image of a group of 6 elements under a homomorphism may have 12 elements. Statement 2 | There is a homomorphism of some group of 6 elements into some group of 12 elements.\\nA) False,... | 16 |
mmlu-abstract-algebra.val.84 | Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective. | ['Please answer with the letter of the correct answer.\n\nLet A and B be sets, f: A -> B and g: B -> A be functions such that for all a \\in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.\nA) False, True\nB) True, True\nC) False, ... | False, True | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"False, True",
"True, True",
"False, False",
"True, False"
]
} | A | A. False, True | B. True, True | C. False, False | D. True, False | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nThe set of all real numbers under the usual multiplication operation is not a group since\nA) multiplication is not associative\nB) zero has no inverse\nC) multiplication is not a binary operation\nD) identity element does not exist\nPrint only a singl... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nThe set of all real numbers under the usual multiplication operation is not a group since\nA) multiplication is not associative\nB) zero has no... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nThe set of all real numbers under the usual multiplication operation is not a group since\\nA) multiplication is not associative\\nB) zero has no inverse\\nC) multiplication is not a binary operation\\... | 16 |
mmlu-abstract-algebra.val.85 | Statement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | A homomorphism is one to one if and only if the kernel consists of the identity element alone. Statement 2 | The image of a group of 6 elements under some homomorphism may have 4 elements.\nA) True, True\nB) False, False\nC) False, True\nD) True, F... | True, False | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"True, True",
"False, False",
"False, True",
"True, False"
]
} | D | D. True, False | A. True, True | B. False, False | C. False, True | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.\nA) False, False\nB) True, False\nC) False, True\nD) True, True\nPrint o... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then ... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | If H is a subgroup of G and a belongs to G then |aH| = |Ha|. Statement 2 | If H is a subgroup of G and a and b belong to G, then aH and Hb are identical or disjoint.\\nA) False, False\\nB... | 16 |
mmlu-abstract-algebra.val.86 | Statement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | If H and K are subgroups of a group G, then |HK| = |H||K|/|H intersection K|. Statement 2 | A group of order 2p where p is an odd prime is cyclic or isomorphic to D_p.\nA) True, False\nB) False, False\nC) False, True\nD) True, True\nPrint only a si... | True, True | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"True, False",
"False, False",
"False, True",
"True, True"
]
} | D | D. True, True | A. True, False | B. False, False | C. False, True | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | Every group of order 159 is cyclic. Statement 2 | Every group of order 102 has a nontrivial proper normal subgroup.\nA) False, False\nB) True, True\nC) False, True\nD) True, False\nPrint only a single choice from "A" or "B" or "C" or "D"... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | Every group of order 159 is cyclic. Statement 2 | Every group of order 102 has a nontrivial proper normal subgroup.\nA) False, Fa... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Every group of order 159 is cyclic. Statement 2 | Every group of order 102 has a nontrivial proper normal subgroup.\\nA) False, False\\nB) True, True\\nC) False, True\\nD) True, False\\nP... | 16 |
mmlu-abstract-algebra.val.87 | For T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2). | ['Please answer with the letter of the correct answer.\n\nFor T: Z x Z -> Z where T(1, 0) = 3 and T(0, 1) = -5, find T(-3,2).\nA) -10\nB) 10\nC) 19\nD) -19\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:'] | -19 | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"-10",
"10",
"19",
"-19"
]
} | D | D. -19 | A. -10 | B. 10 | C. 19 | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nIdentify a solution for the equation 5x β 5 = β10 from the given numbers.\nA) β6\nB) β1\nC) β3\nD) β4\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:']
Solution:
B
Question:
['Please answer with the letter of the... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nIdentify a solution for the equation 5x β 5 = β10 from the given numbers.\nA) β6\nB) β1\nC) β3\nD) β4\nPrint only a single choice from "A" or ... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nIdentify a solution for the equation 5x β 5 = β10 from the given numbers.\\nA) β6\\nB) β1\\nC) β3\\nD) β4\\nPrint only a single choice from \"A\" or \"B\" or \"C\" or \"D\" without explanation. Answer... | 16 |
mmlu-abstract-algebra.val.88 | Compute the product in the given ring. (12)(16) in Z_24 | ['Please answer with the letter of the correct answer.\n\nCompute the product in the given ring. (12)(16) in Z_24\nA) 1\nB) 6\nC) 4\nD) 0\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:'] | 0 | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"6",
"4",
"0"
]
} | D | D. 0 | A. 1 | B. 6 | C. 4 | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nCompute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9\nA) (3,6)\nB) (3,1)\nC) (1,1)\nD) (1,6)\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:']
Solution:
D
Question:
['Please answer with the letter of th... | Instruction: Directly output the answer to the last question. Do not summarize or list any previous answers.
Question:
['Please answer with the letter of the correct answer.\n\nCompute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9\nA) (3,6)\nB) (3,1)\nC) (1,1)\nD) (1,6)\nPrint only a single choice from "A" or... | [
{
"retrieved_answer": "D",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nCompute the product in the given ring. (2,3)(3,5) in Z_5 x Z_9\\nA) (3,6)\\nB) (3,1)\\nC) (1,1)\\nD) (1,6)\\nPrint only a single choice from \"A\" or \"B\" or \"C\" or \"D\" without explanation. Answe... | 16 |
mmlu-abstract-algebra.val.89 | "Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permuta(...TRUNCATED) | "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Every permutation is a on(...TRUNCATED) | True, False | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"False, True",
"True, False",
"False, False",
"True, True"
]
} | B | B. True, False | A. False, True | C. False, False | D. True, True | mmlu-abstract-algebra | "Question:\n['Please answer with the letter of the correct answer.\\n\\nStatement 1 | The homomorphi(...TRUNCATED) | "Instruction: Directly output the answer to the last question. Do not summarize or list any previous(...TRUNCATED) | [{"retrieved_answer":"B","retrieved_query":"['Please answer with the letter of the correct answer.\\(...TRUNCATED) | 16 |
mmlu-abstract-algebra.val.9 | "Find all zeros in the indicated finite field of the given polynomial with coefficients in that fiel(...TRUNCATED) | "['Please answer with the letter of the correct answer.\\n\\nFind all zeros in the indicated finite (...TRUNCATED) | 2,3 | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"1",
"2,3",
"2",
"6"
]
} | B | B. 2,3 | A. 1 | C. 2 | D. 6 | mmlu-abstract-algebra | "Question:\n['Please answer with the letter of the correct answer.\\n\\nFind the degree for the give(...TRUNCATED) | "Instruction: Directly output the answer to the last question. Do not summarize or list any previous(...TRUNCATED) | [{"retrieved_answer":"C","retrieved_query":"['Please answer with the letter of the correct answer.\\(...TRUNCATED) | 16 |
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