GATE | GATE-CS-2000 | Question 29

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

(A) a
(B) b
(C) c
(D) d
(E) None


Answer: (E)

Explanation: (B) false, consider, S={a,{a}};
P(S) = {∅,{a},{{a}},{a,{a}}}
P(P(S)) = {∅,{{a}}, …}
And so P(S)∩P(P(S))⊃{∅,{{a}}}.

Consider {Ø} set as counter example of other options.

None are correct.

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