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

GATE · 2000 · CS · Question 2 subparts· Modified — slightly modified from the official paper; see the solution

1. A.

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

2. B.

   ∅ ∈ P(S) ∩ P(P(S))

3. C.

   P(S) ∩ S = P(S)

4. D.

   S ∉ P(S)

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