Question 3: a. Let (H,+) ≤ (R, +), let K = {2h : h E H}. Prove that (K,x) ≤ (R*,x). (Clarification: the notations +,x are addition and multiplication operations respectively). b. Let H = {a + bi: ab ≥ 0 and a, b E R}. Explain why H is not a subgroup of C under addition. (Clarification: the notation C is the set of complex numbers).

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