Let P(S) denotes the power set of set S. Which of the following is always true?

2000

Answer: B. P(S) ∩ P(P(S))={ϕ} — The power set P(S) contains all subsets of S. For any set S, P(P(S)) contains sets of subsets.

1. A.

   P(P(S))=P(S)

2. B.

   P(S) ∩ P(P(S))={ϕ}

3. C.

   P(S)∩S=P(S)

4. D.

   S∉P(S)

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