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In each of the following, prove that the specified subset H is a subgroup of the...

In each of the following, prove that the specified subset H is a subgroup of the given group G. Note: in each case, you may assume that the given operation is associative. (a) G = (C ∗ , ·), H is the set of complex numbers of norm 1; i.e., the unit circle in the complex plane. (b) G = (Q, +), for fixed n, H is the set of rational numbers whose denominators divide n. (c) G = (Dn, ◦), H = the set of all rotations in G.

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