Suppose G is an abelian group and let S = {a e Gax for some x = G} = be the set of squares in G. Prove that S is a subgroup of G. Part b: Calculate the set S for D5. Prove that it is a subgroup, and explain why your proof from Part a does not apply to this part. Part c: Do you think you can prove a more general statement about when the set of squares S is a subgroup of a group G? State a conjecture about a generalization of Part a to non-abelian groups, and write 2-3 sentences explaining your intuition. (You do not have to come up with a proof, but Part a and Part b together should suggest to you that Part a is not the complete story.)