Question: Find the order of the factor group (Z_4 x Z_12)/(<2> x <2>)
Choices:
A. 2
B. 3
C. 4
D. 12
Answer: 4

Question: Statement 1 | Every integral domain has a field of quotients. Statement 2 | A polynomial of degree n over a ring can have at most n zeros counting multiplicity.
Choices:
A. True, True
B. False, False
C. True, False
D. False, True
Answer: True, False

Question: Statement 1 | The symmetric group S_3 is cyclic. Statement 2 | Every group is isomorphic to some group of permutations.
Choices:
A. True, True
B. False, False
C. True, False
D. False, True
Answer: False, 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.
Choices:
A. True, True
B. False, False
C. True, False
D. False, True
Answer: There should be exactly 5 paragraphs separated by the markdown divider: ***.
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