[["Question: Statement 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.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, True"],["Question: Statement 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.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, False"],["Question: Statement 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.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, False"],["Question: Statement 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.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, True"],["Question: Find the characteristic of the ring Z_3 x 3Z.\nChoices:\nA. 0\nB. 3\nC. 12\nD. 30\nAnswer:"," 0"],["Question: Find the characteristic of the ring Z_3 x 3Z.\nChoices:\nA. 0\nB. 3\nC. 12\nD. 30\nAnswer:"," 3"],["Question: Find the characteristic of the ring Z_3 x 3Z.\nChoices:\nA. 0\nB. 3\nC. 12\nD. 30\nAnswer:"," 12"],["Question: Find the characteristic of the ring Z_3 x 3Z.\nChoices:\nA. 0\nB. 3\nC. 12\nD. 30\nAnswer:"," 30"],["Question: Find all cosets of the subgroup 4Z of 2Z.\nChoices:\nA. 4Z\nB. 4Z, 2 + 4Z\nC. 2Z\nD. Z\nAnswer:"," 4Z"],["Question: Find all cosets of the subgroup 4Z of 2Z.\nChoices:\nA. 4Z\nB. 4Z, 2 + 4Z\nC. 2Z\nD. Z\nAnswer:"," 4Z, 2 + 4Z"],["Question: Find all cosets of the subgroup 4Z of 2Z.\nChoices:\nA. 4Z\nB. 4Z, 2 + 4Z\nC. 2Z\nD. Z\nAnswer:"," 2Z"],["Question: Find all cosets of the subgroup 4Z of 2Z.\nChoices:\nA. 4Z\nB. 4Z, 2 + 4Z\nC. 2Z\nD. Z\nAnswer:"," Z"],["Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7\nChoices:\nA. 1\nB. 2\nC. 2,3\nD. 6\nAnswer:"," 1"],["Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7\nChoices:\nA. 1\nB. 2\nC. 2,3\nD. 6\nAnswer:"," 2"],["Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7\nChoices:\nA. 1\nB. 2\nC. 2,3\nD. 6\nAnswer:"," 2,3"],["Question: Find all zeros in the indicated finite field of the given polynomial with coefficients in that field. x^3 + 2x + 2 in Z_7\nChoices:\nA. 1\nB. 2\nC. 2,3\nD. 6\nAnswer:"," 6"],["Question: Statement 1 | Every field is also a ring. Statement 2 | Every ring has a multiplicative identity.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, True"],["Question: Statement 1 | Every field is also a ring. Statement 2 | Every ring has a multiplicative identity.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, False"],["Question: Statement 1 | Every field is also a ring. Statement 2 | Every ring has a multiplicative identity.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, False"],["Question: Statement 1 | Every field is also a ring. Statement 2 | Every ring has a multiplicative identity.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, True"],["Question: Statement 1 | Every solvable group is of prime-power order. Statement 2 | Every group of prime-power order is solvable.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, True"],["Question: Statement 1 | Every solvable group is of prime-power order. Statement 2 | Every group of prime-power order is solvable.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, False"],["Question: Statement 1 | Every solvable group is of prime-power order. Statement 2 | Every group of prime-power order is solvable.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, False"],["Question: Statement 1 | Every solvable group is of prime-power order. Statement 2 | Every group of prime-power order is solvable.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, True"],["Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\nChoices:\nA. 8\nB. 2\nC. 24\nD. 120\nAnswer:"," 8"],["Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\nChoices:\nA. 8\nB. 2\nC. 24\nD. 120\nAnswer:"," 2"],["Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\nChoices:\nA. 8\nB. 2\nC. 24\nD. 120\nAnswer:"," 24"],["Question: Let p = (1, 2, 5, 4)(2, 3) in S_5 . Find the index of <p> in S_5.\nChoices:\nA. 8\nB. 2\nC. 24\nD. 120\nAnswer:"," 120"],["Question: (Z,*) is a group with a*b = a+b+1 for all a, b in Z. The inverse of a is\nChoices:\nA. 0\nB. -2\nC. a-2\nD. (2+a)*-1\nAnswer:"," 0"],["Question: (Z,*) is a group with a*b = a+b+1 for all a, b in Z. The inverse of a is\nChoices:\nA. 0\nB. -2\nC. a-2\nD. (2+a)*-1\nAnswer:"," -2"],["Question: (Z,*) is a group with a*b = a+b+1 for all a, b in Z. The inverse of a is\nChoices:\nA. 0\nB. -2\nC. a-2\nD. (2+a)*-1\nAnswer:"," a-2"],["Question: (Z,*) is a group with a*b = a+b+1 for all a, b in Z. The inverse of a is\nChoices:\nA. 0\nB. -2\nC. a-2\nD. (2+a)*-1\nAnswer:"," (2+a)*-1"],["Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, True"],["Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, False"],["Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, False"],["Question: Statement 1 | R is a splitting field of some polynomial over Q. Statement 2 | There is a field with 60 elements.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, True"],["Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, True"],["Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, False"],["Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," True, False"],["Question: Statement 1 | For n > 1, the set {1,2, ..., n-1} is a group under multiplication modulo n. Statement 2 | There is an integer x such that 63x mod 100 = 1.\nChoices:\nA. True, True\nB. False, False\nC. True, False\nD. False, True\nAnswer:"," False, True"]]
