Question

if set A ={1,3,5} , then number of elements in P{P(A)} is (a)8 (b)256 (c) 248 (d) 250​

Answer 1

number of elements in {P(A)} = 2^n = 2^3 = 8

number of elements in P{P(A)} = 2^8 = 256

(b)256

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If A = {1,3,5} , then number of elements in P{P(A)} is

(a) 8

(b) 256

(c) 248

(d) 250

EVALUATION

We know that set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

Again for a set A the power set of A is defined as the set of all subsets of A and denoted by P(A)

Also if A contains n elements then the number of elements in P(A) =

$\sf{ = {2}^{n} }$

Here the given set is A = { 1 , 3 , 5 }

Number of elements in A = 3

The number of elements in P(A)

$\sf{ = {2}^{3} }$

$= 8$

The number of elements in P(P(A))

$\sf{ = {2}^{8} }$

$\bf{ = 256}$

FINAL ANSWER

Hence the correct option is (b) 256

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