Discussion
Let a * H and b * H be two cosets of H.
(i) Either a * H and b * H are disjoint
(ii) a * H and b * H are identical Then,
Answer: C
Two left cosets of a subgroup H are either identical or disjoint: if they have an element in common, say c, then each of them equals the coset of c, so they are the same coset. So for any a and b one of the two statements, (i) or (ii), must hold, and the answer is '(i) or (ii) is true', option (C). 'Only (i)' and 'only (ii)' are wrong because either case can occur depending on the choice of a and b, and '(i) and (ii) is false' is impossible because the cosets must be one or the other.
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