question
stringclasses 5
values | option1
stringclasses 2
values | option2
stringclasses 3
values | option3
stringclasses 3
values | option4
stringclasses 3
values | answer
stringclasses 3
values |
|---|---|---|---|---|---|
Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field. | 0 | 1 | 2 | 3 | B |
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. | True, True | False, False | True, False | False, True | B |
Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements. | True, True | False, False | True, False | False, True | C |
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. | True, True | False, False | True, False | False, True | A |
Find the characteristic of the ring 2Z. | 0 | 3 | 12 | 30 | A |
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