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

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

  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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Correct answer: B

The power set P(S) contains all subsets of S. For any set S, P(P(S)) contains sets of subsets.

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