Question

If A be a finite set of size n, then number of elements in the power set of A x A
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Answer 1

Step-by-step explanation:

Let A be a finite set of size n the number of power set of AxA is 2^n2.

The power set of a set A is the collection of all subsets of A. It contains every possible subset of A, including the empty set and the set A itself.

The power set of any set S is the set of all subsets of S, including the empty set and S itself, variously denoted as P(S).

Answer 2

Given,

A be a set of size n.

Solution.

Calculate the number of elements in the power set $\[A \times A\]$.

It is given that A be a set of size n. It means set A has n number of elements.

Number of elements in the power set A,

$\[ = {2^n}\]$

Number of elements in the power set $\[A \times A\]$,

$\[ = {2^{{2^n}}}\]$

Hence the number of elements in the power set $\[A \times A\]$ is $\[{2^{{2^n}}}\]$