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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