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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