Question

Q) A = { 1 , 2 , 3 , 4 , 5 }
What is the number of subsets in P(P(P(P(P(P(A)))))) ?
Provide an easy solution !

Answer 1

Hello !
See the number of sets in A is = 5 = n
Number of subsets in any set is given by the formula 2^n
Where n is the number of elements
P denotes Power set 
A power set is a set of all the subsets of a set 
The number of elements of a Power set P(A) of A is 2^n
And the number of elements of in P(P(A)) = 2^2^n
Therefore , 
The number of elements in P(P(P(P(P(P(A))))) = 2^2^2^2^2^2^n 
⇒ 2^2^2^2^2^2^5 
= 2^2^2^2^2^32
= 2^2^2^2^4294967296 = x
Now the number of elements in P(P(P(P(P(P(A))))) is x 
And the number of subsets of P(P(P(P(P(P(A)))))  =  2^x
And hence, the answer would be nearly infinity
And so the answer is ∞                                Ans.
I hope my answer is correct !!