| {"doc": {"question": "Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.", "subject": "abstract_algebra", "choices": ["A", "B", "C", "D"], "answer": 1, "index": 0, "query": "Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.\n A. 0\n B. 4\n C. 2\n D. 6\nAnswer:", "gold": 1}, "task_name": "mmlu_abstract_algebra:mc", "doc_id": 0, "native_id": 0, "label": 1, "requests": [{"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.\n A. 0\n B. 4\n C. 2\n D. 6\nAnswer:", "continuation": " A"}, "idx": 0}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.\n A. 0\n B. 4\n C. 2\n D. 6\nAnswer:", "continuation": " B"}, "idx": 1}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.\n A. 0\n B. 4\n C. 2\n D. 6\nAnswer:", "continuation": " C"}, "idx": 2}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.\n A. 0\n B. 4\n C. 2\n D. 6\nAnswer:", "continuation": " D"}, "idx": 3}]} | |
| {"doc": {"question": "Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.", "subject": "abstract_algebra", "choices": ["A", "B", "C", "D"], "answer": 2, "index": 1, "query": "Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\n A. 8\n B. 2\n C. 24\n D. 120\nAnswer:", "gold": 2}, "task_name": "mmlu_abstract_algebra:mc", "doc_id": 1, "native_id": 1, "label": 2, "requests": [{"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\n A. 8\n B. 2\n C. 24\n D. 120\nAnswer:", "continuation": " A"}, "idx": 0}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\n A. 8\n B. 2\n C. 24\n D. 120\nAnswer:", "continuation": " B"}, "idx": 1}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\n A. 8\n B. 2\n C. 24\n D. 120\nAnswer:", "continuation": " C"}, "idx": 2}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\n A. 8\n B. 2\n C. 24\n D. 120\nAnswer:", "continuation": " D"}, "idx": 3}]} | |
| {"doc": {"question": "Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5", "subject": "abstract_algebra", "choices": ["A", "B", "C", "D"], "answer": 3, "index": 2, "query": "Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5\n A. 0\n B. 1\n C. 0,1\n D. 0,4\nAnswer:", "gold": 3}, "task_name": "mmlu_abstract_algebra:mc", "doc_id": 2, "native_id": 2, "label": 3, "requests": [{"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5\n A. 0\n B. 1\n C. 0,1\n D. 0,4\nAnswer:", "continuation": " A"}, "idx": 0}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5\n A. 0\n B. 1\n C. 0,1\n D. 0,4\nAnswer:", "continuation": " B"}, "idx": 1}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5\n A. 0\n B. 1\n C. 0,1\n D. 0,4\nAnswer:", "continuation": " C"}, "idx": 2}, {"request_type": "loglikelihood", "request": {"context": "The following are multiple choice questions (with answers) about abstract algebra.\n\nQuestion: Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.\n A. 0\n B. 1\n C. 2\n D. 3\nAnswer: B\n\nQuestion: Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: B\n\nQuestion: Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: C\n\nQuestion: Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.\n A. True, True\n B. False, False\n C. True, False\n D. False, True\nAnswer: A\n\nQuestion: Find the characteristic of the ring 2Z.\n A. 0\n B. 3\n C. 12\n D. 30\nAnswer: A\n\nQuestion: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^5 + 3x^3 + x^2 + 2x in Z_5\n A. 0\n B. 1\n C. 0,1\n D. 0,4\nAnswer:", "continuation": " D"}, "idx": 3}]} | |