GATE CSE 1995 | Question: 1.20

Question

The number of elements in the power set $P(S)$ of the set $S=\{\{\emptyset\}, 1, \{2, 3\}\}$ is:

• A. $2$
• B. $4$
• C. $8$
• D. None of the above

Comments

@Abhisek Tiwari 4

Then the elements will be as

{∅,{∅},{1},{{2,3}},{∅,1},{1,{2,3}},{∅,{2,3}},{∅,1,{2,3}}}..

Then {∅,1} and {1} are they not equal?

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@BharathiCH 

Yes {1} and { {∅},1} different. [Note it should be {{∅},1} instead of {∅,1}

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It is explicitly said in the question that what ever S is, it a set according to paper setter, so we just need to calculate the cardinality and apply the formula.

Answer 1

S = {(φ), 1, (2, 3)}

number of elements in set = 3

cardinality of Power set of S = 2^number of elements in set

                                             = 2^3

                                             = 8

I hope my answer helps you a lot

Answer 2

Answer is option (C)

-> Power set works on the basis of TAKE/NOT TAKE that will end up creating two possibilities for the every element in the set. Represented in the form of 2^n.(n:number of elements in the set).

2^n=2^3=8.