Question

If A = {1,2,3,4} and P(A) represents power set
of A, then n(P(P(A))) is​

Answer 1

Step-by-step explanation:

If A = {1,2,3,4}

then P(A)= 2⁴ = 16

now P(A) has 16 elements and

so n(P(P(A)))= 2¹⁶ i.e. P(P(A)) has 2×2×2...×16times elements

Answer 2

The value of n(P(P(A))) = 65536

Given:

A = {1,2,3,4} and P(A) represents power set (A)

To find:

The n(P(P(A)))

Solution:

Given  A = { 1, 2, 3, 4 }

The power set:

The power set of a set is a set which includes all the subsets and the original set itself. It is usually denoted by P

The formula for the power set of A is $2^{n(A)}$  

⇒ P (A) = $2^{n(A)}$  

Here,  P refers the power set

n(A) = Number of elements in set A  

From given data n(A) = 4

⇒  P (A) = $2^{n(A)}$  

⇒  P(A) = 2⁴ = 16

Number of elements in P(A) = 16

Then  n(P(P(A))) = 2¹⁶ = 65536

Therefore, the value of n(P(P(A))) = 65536

#SPJ2