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 1.92k 20.5k | concatenated_prompt stringlengths 2.25k 23.5k | retrieved_examples listlengths 8 8 | num_demonstrations int64 8 8 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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... | 8 |
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... | 8 |
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 | Some abelian group of order 45 has a subgroup of order 10. Statement 2 | A subgroup H of a group G is a normal subgroup if and only if thenumber of left cosets of H is equal to the number of right cosets of H.\nA) True, False\nB) False, T... | 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 | Some abelian group of order 45 has a subgroup of order 10. Statement 2 | A subgroup H of a group G is a normal subgroup if and on... | [
{
"retrieved_answer": "D",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Some abelian group of order 45 has a subgroup of order 10. Statement 2 | A subgroup H of a group G is a normal subgroup if and only if thenumber of left cosets of H is equal to the number... | 8 |
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\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 f must necessarily be injective. Statement 2 | The function f must necessarily be surjective.\nA) True, True\nB) False, 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\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 f must necessaril... | [
{
"retrieved_answer": "D",
"retrieved_query": "['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 f must necessarily be injective. Statement 2 | The function f must necess... | 8 |
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 | A homomorphism may have an empty kernel. Statement 2 | It is not possible to have a nontrivial homomorphism of some finite group into some infinite group.\nA) False, True\nB) False, False\nC) True, True\nD) True, False\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\nStatement 1 | A homomorphism may have an empty kernel. Statement 2 | It is not possible to have a nontrivial homomorphism of some finite group ... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | A homomorphism may have an empty kernel. Statement 2 | It is not possible to have a nontrivial homomorphism of some finite group into some infinite group.\\nA) False, True\\nB) False, Fal... | 8 |
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 | 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... | 8 |
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\nPoint A and point B are placed on a numberline. Point A is located at -20 and point B is 5 less than point A. Which statement about point B is true?\nA) It is located at -15 and is to the left of point A on the numberline.\nB) It is located at -25 and ... | 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\nPoint A and point B are placed on a numberline. Point A is located at -20 and point B is 5 less than point A. Which statement about point B is ... | [
{
"retrieved_answer": "D",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nPoint A and point B are placed on a numberline. Point A is located at -20 and point B is 5 less than point A. Which statement about point B is true?\\nA) It is located at -15 and is to the left of poin... | 8 |
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\nFind the generator for the finite field Z_11.\nA) 1\nB) 4\nC) 3\nD) 2\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 the correct answer.\n\nCompute 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\nFind the generator for the finite field Z_11.\nA) 1\nB) 4\nC) 3\nD) 2\nPrint only a single choice from "A" or "B" or "C" or "D" without explan... | [
{
"retrieved_answer": "D",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nFind the generator for the finite field Z_11.\\nA) 1\\nB) 4\\nC) 3\\nD) 2\\nPrint only a single choice from \"A\" or \"B\" or \"C\" or \"D\" without explanation. Answer:']",
"score": 0.70347136259... | 8 |
mmlu-abstract-algebra.val.89 | Statement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | Every permutation is a one-to-one function. Statement 2 | Every function is a permutation if and only if it is one to one.\nA) False, True\nB) True, False\nC) False, False\nD) True, True\nPrint only a single choice from "A" or "B" or "C" or "D" wi... | 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:
['Please answer with the letter of the correct answer.\n\nStatement 1 | Every solvable group is of prime-power order. Statement 2 | Every group of prime-power order is solvable.\nA) False, False\nB) False, True\nC) True, True\nD) True, False\nPrint only a single choice from "A" or "B" or "C" or "D" without e... | 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 solvable group is of prime-power order. Statement 2 | Every group of prime-power order is solvable.\nA) False, False\nB) Fa... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Every solvable group is of prime-power order. Statement 2 | Every group of prime-power order is solvable.\\nA) False, False\\nB) False, True\\nC) True, True\\nD) True, False\\nPrint only ... | 8 |
mmlu-abstract-algebra.val.9 | Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7 | ['Please answer with the letter of the correct answer.\n\nFind all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7\nA) 1\nB) 2,3\nC) 2\nD) 6\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:'] | 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:
['Please answer with the letter of the correct answer.\n\nFind the generator for the finite field Z_7.\nA) 3\nB) 1\nC) 2\nD) 4\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:']
Solution:
A
Question:
['Please answer with the letter of the correct answer.\n\nFind all c in... | 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\nFind the generator for the finite field Z_7.\nA) 3\nB) 1\nC) 2\nD) 4\nPrint only a single choice from "A" or "B" or "C" or "D" without explana... | [
{
"retrieved_answer": "A",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nFind the generator for the finite field Z_7.\\nA) 3\\nB) 1\\nC) 2\\nD) 4\\nPrint only a single choice from \"A\" or \"B\" or \"C\" or \"D\" without explanation. Answer:']",
"score": 0.815186321735... | 8 |
mmlu-abstract-algebra.val.90 | Statement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | If a finite group has order n then the group contains a subgroup of order d for every positive divisor d of n. Statement 2 | If a belongs to a finite group then |a| divides |G|.\nA) False, True\nB) True, False\nC) False, False\nD) True, True\nPrint... | False, True | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"False, True",
"True, False",
"False, False",
"True, True"
]
} | A | A. False, True | B. True, False | C. False, False | D. True, True | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.\nA) True, True\nB) False, True\nC) False, False\nD) True, False\nPrint only a single choice from "A" or "B"... | 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 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.... | [
{
"retrieved_answer": "D",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Every group of order 42 has a normal subgroup of order 7. Statement 2 | Every group of order 42 has a normal subgroup of order 8.\\nA) True, True\\nB) False, True\\nC) False, False\\nD) T... | 8 |
mmlu-abstract-algebra.val.91 | Find all cosets of the subgroup 4Z of 2Z. | ['Please answer with the letter of the correct answer.\n\nFind all cosets of the subgroup 4Z of 2Z.\nA) 2Z\nB) Z\nC) 4Z\nD) 4Z, 2 + 4Z\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:'] | 4Z, 2 + 4Z | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2Z",
"Z",
"4Z",
"4Z, 2 + 4Z"
]
} | D | D. 4Z, 2 + 4Z | A. 2Z | B. Z | C. 4Z | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nA subset H of a group (G,*) is a group if\nA) a,b in H=> a * b^-1 in H\nB) a in H => a^-1 in H\nC) H contains the identity element\nD) a,b in H=> a * b in H\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:']
Solut... | 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\nA subset H of a group (G,*) is a group if\nA) a,b in H=> a * b^-1 in H\nB) a in H => a^-1 in H\nC) H contains the identity element\nD) a,b in H... | [
{
"retrieved_answer": "A",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nA subset H of a group (G,*) is a group if\\nA) a,b in H=> a * b^-1 in H\\nB) a in H => a^-1 in H\\nC) H contains the identity element\\nD) a,b in H=> a * b in H\\nPrint only a single choice from \"A\"... | 8 |
mmlu-abstract-algebra.val.92 | Which of the following statements is true? | ['Please answer with the letter of the correct answer.\n\nWhich of the following statements is true?\nA) Number of relations form A = {x, y, z} to B= (1, 2), is 64.\nB) Properties of a relation being symmetric and being un-symmetric are negative of each other.\nC) Every equivalence relation is a partial-ordering relati... | Number of relations form A = {x, y, z} to B= (1, 2), is 64. | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"Number of relations form A = {x, y, z} to B= (1, 2), is 64.",
"Properties of a relation being symmetric and being un-symmetric are negative of each other.",
"Every equivalence relation is a partial-ordering relation.",
"Empty relation _... | A | A. Number of relations form A = {x, y, z} to B= (1, 2), is 64. | B. Properties of a relation being symmetric and being un-symmetric are negative of each other. | C. Every equivalence relation is a partial-ordering relation. | D. Empty relation _ is reflexive | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nWhich of the following are true:\nA) It is possible to place a linear order relation on the complex numbers C which make (C, +, ×, ≤) an ordered field.\nB) It is possible to place an linear order relation ≤ on the complex numbers C such that (C, +, ×, ... | 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\nWhich of the following are true:\nA) It is possible to place a linear order relation on the complex numbers C which make (C, +, ×, ≤) an ordere... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nWhich of the following are true:\\nA) It is possible to place a linear order relation on the complex numbers C which make (C, +, ×, ≤) an ordered field.\\nB) It is possible to place an linear order rel... | 8 |
mmlu-abstract-algebra.val.93 | Find the maximum possible order for an element of S_n for n = 6. | ['Please answer with the letter of the correct answer.\n\nFind the maximum possible order for an element of S_n for n = 6.\nA) 30\nB) 105\nC) 6\nD) 12\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:'] | 6 | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"30",
"105",
"6",
"12"
]
} | C | C. 6 | A. 30 | B. 105 | D. 12 | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nWhat is the largest order of an element in the group of permutations of 5 objects?\nA) 5\nB) 15\nC) 12\nD) 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... | 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\nWhat is the largest order of an element in the group of permutations of 5 objects?\nA) 5\nB) 15\nC) 12\nD) 6\nPrint only a single choice from ... | [
{
"retrieved_answer": "D",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nWhat is the largest order of an element in the group of permutations of 5 objects?\\nA) 5\\nB) 15\\nC) 12\\nD) 6\\nPrint only a single choice from \"A\" or \"B\" or \"C\" or \"D\" without explanation.... | 8 |
mmlu-abstract-algebra.val.94 | Statement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field. | ['Please answer with the letter of the correct answer.\n\nStatement 1 | Q is an extension field of Z_2. Statement 2 | Every non-constant polynomial over a field has a zero in some extension field.\nA) True, False\nB) False, False\nC) True, True\nD) False, True\nPrint only a single choice from "A" or "B" or "C" or "D" ... | False, True | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"True, False",
"False, False",
"True, True",
"False, True"
]
} | D | D. False, True | A. True, False | B. False, False | C. True, True | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.\nA) False, True\nB) True, False\nC) False, False\nD) True, True\nPrint only a single choice from "A" or "B" or "C" or "D" without explanat... | 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 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.\nA) False, True\nB) True, Fals... | [
{
"retrieved_answer": "C",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.\\nA) False, True\\nB) True, False\\nC) False, False\\nD) True, True\\nPrint only a singl... | 8 |
mmlu-abstract-algebra.val.95 | Statement 1 | If H is a subgroup of G and a belongs to G then aH is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H. | ['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 is a subgroup of G if and only if a is in H. Statement 2 | If H is a subgroup of G and a and b belong to G then aH = bH if and only if ab is in H.\nA) False, False\nB) True, True\nC) False, True\nD... | True, False | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"False, False",
"True, True",
"False, True",
"True, False"
]
} | D | D. True, False | A. False, False | B. True, True | C. False, True | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nStatement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.\nA) True, True\nB) False, False\nC) True, False\nD) F... | 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 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n... | [
{
"retrieved_answer": "A",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | For finite groups G and H, |G + H| = |G||H|. (G + H is the internal direct product.) Statement 2 | If r divides m and s divides n then Z_m + Z_n has a subgroup isomorphic to Z_r + Z_s.\\n... | 8 |
mmlu-abstract-algebra.val.96 | Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2 | ['Please answer with the letter of the correct answer.\n\nFind all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^2 + 1 in Z_2\nA) 2\nB) 0\nC) 1\nD) 0,1\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:'] | 1 | {
"label": [
"A",
"B",
"C",
"D"
],
"text": [
"2",
"0",
"1",
"0,1"
]
} | C | C. 1 | A. 2 | B. 0 | D. 0,1 | mmlu-abstract-algebra | Question:
['Please answer with the letter of the correct answer.\n\nFind the generator for the finite field Z_7.\nA) 3\nB) 1\nC) 2\nD) 4\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:']
Solution:
A
Question:
['Please answer with the letter of the correct answer.\n\nThe polynomia... | 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\nFind the generator for the finite field Z_7.\nA) 3\nB) 1\nC) 2\nD) 4\nPrint only a single choice from "A" or "B" or "C" or "D" without explana... | [
{
"retrieved_answer": "A",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nFind the generator for the finite field Z_7.\\nA) 3\\nB) 1\\nC) 2\\nD) 4\\nPrint only a single choice from \"A\" or \"B\" or \"C\" or \"D\" without explanation. Answer:']",
"score": 0.715927779674... | 8 |
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