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