f A={1,2}, p(A) denotes power set of A, then the number of elements in P(P(P(P(A)))) is - Maths - Sets

Question

f A={1,2}, p(A) denotes power set of A, then the number of elements
in P(P(P(P(A)))) is

Atul Shaw · Accepted Answer

Dear student,A=1,2For a given set S with n elements, number of elements inP(S)is 2n
As each element has two possibilities(present or absent},possible subsets are 2×2×2
ntimes=2n
 Therefore, power setcontains 2n elements
P(A)=22=4Now, we can say P(A) has 4 element
P(P(A))=24=16P(P(P(A)))=216P(P(P(P(A))))=2216Regards