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 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.\nA) False, True\nB) True, False\nC) False, False\nD) ... | 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 homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are ... | [
{
"retrieved_answer": "D",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Every homomorphic image of a group G is isomorphic to a factor group of G. Statement 2 | The homomorphic images of a group G are the same (up to isomorphism) as the factor groups of G.\\n... | 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 set of 2 x 2 matrices with integer entries and nonzero determinant is a group under matrix multiplication. Statement 2 | The set of 2 x 2 matrices with integer entries and determinant 1 is a group under matrix multiplication.\nA) Fals... | 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 set of 2 x 2 matrices with integer entries and nonzero determinant is a group under matrix multiplication. Statement 2 | The ... | [
{
"retrieved_answer": "A",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | The set of 2 x 2 matrices with integer entries and nonzero determinant is a group under matrix multiplication. Statement 2 | The set of 2 x 2 matrices with integer entries and determinant... | 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\nStatement 1 | Suppose β|a_i| diverges and β a_i = 2. There is a rearrangement a_i_k of the terms such that β a_i_k = 4. Statement 2 | There exists metric spaces X and Y with X closed and bounded and a continuous mapping f : X β Y such that f(X) is NOT... | 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 | Suppose β|a_i| diverges and β a_i = 2. There is a rearrangement a_i_k of the terms such that β a_i_k = 4. Statement 2 | There ex... | [
{
"retrieved_answer": "C",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Suppose β|a_i| diverges and β a_i = 2. There is a rearrangement a_i_k of the terms such that β a_i_k = 4. Statement 2 | There exists metric spaces X and Y with X closed and bounded and a... | 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 | Every quotient ring of every commutative ring is again a commutative ring. Statement 2 | An ideal N in a ring R with unity 1 is all of R if and only if 1 in N.\nA) True, True\nB) True, False\nC) False, True\nD) False, False\nPrint only a ... | 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 quotient ring of every commutative ring is again a commutative ring. Statement 2 | An ideal N in a ring R with unity 1 is a... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1 | Every quotient ring of every commutative ring is again a commutative ring. Statement 2 | An ideal N in a ring R with unity 1 is all of R if and only if 1 in N.\\nA) True, True\\nB) True, ... | 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 p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subgroup of G.\nA) False, False\nB) True, True\nC) True... | 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 p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a norma... | [
{
"retrieved_answer": "B",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nStatement 1| Every group of order p^2 where p is prime is Abelian. Statement 2 | For a fixed prime p a Sylow p-subgroup of a group G is a normal subgroup of G if and only if it is the only Sylow p-subg... | 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\nFind the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].\nA) x^2 + 1\nB) 0\nC) 2x^2 + 5\nD) 6x^2 + 4x + 6\nPrint only a single choice from "A" or "B" or "C" or "D" without explanation. Answer:'... | 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 sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].\nA) x^2 + 1\nB) 0\nC) 2x^2 +... | [
{
"retrieved_answer": "C",
"retrieved_query": "['Please answer with the letter of the correct answer.\\n\\nFind the sum of the given polynomials in the given polynomial ring. f(x) = 4x - 5, g(x) = 2x^2 - 4x + 2 in Z_8[x].\\nA) x^2 + 1\\nB) 0\\nC) 2x^2 + 5\\nD) 6x^2 + 4x + 6\\nPrint only a single choice fro... | 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 image of a(...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 product of the give(...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 |
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