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60 votes
60 votes

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

  1. $P(P(S)) = P(S)$
  2. $P(S) ∩ P(P(S)) = \{ Ø \}$
  3. $P(S) ∩ S = P(S)$
  4. $S ∉ P(S)$
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6 Answers

3 votes
3 votes
Let S = {1,2}

P(S) = {{},(1,1),(1,2),(2,1),(2,2)}

P(P(S)) = {{} , (1,1,1,1) , (1,1,1,2) , (1,1,2,1) , (1,1,2,2)...................................... }

So , intersection of P(S) and P(P(S)) = phi

 

Please correct me , if my understanding is wrong.
0 votes
0 votes

ϕ always present in any power set of a set and ϕ is the only common element between P(S) and P(P(S))

Therefore, 

P(S)  ∩  P(P(S) = {ϕ}

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Answer:

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