For a set S, we defined P(S) to be the set containing exactly the subsets of S. Do your best to give a proof of the following results. 1. Prove that if P(S) has one element, then S = 0. 2. Let A be a set. Prove that N S= 0. SEP(A) 3. Let A and B be sets. Prove that if A C B, then P(A) C P(B). 4. Prove that if A and B are sets, then P(A) U P(B) C P(AU B).

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Q: Let A be a set. Prove that S = 0. SEP(A)

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A: Solution is given below:

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