Let G and H be groups and let :G →H be a homomorphism. a) Prove that (G), the image of p, is a subgroup of H. (Hint: Use the fact that ø(g¯¹)=ø(g)¯¹ for any g in G) b) Prove that if is one-to-one, then G = (G).

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…