Question

If $A=\left\{1,2,3\right\}$, the number of elements in a power set is __________.

Answer 1

Finding the elements of a Power set:

Power set: The set containing the possible subsets of a set A is called the power set of set A. It is denoted by P(A).

$A=\left\{1,2,3\right\}$

Here, the number of subsets of A are $2^3=8thatis\left\{\right\},\left\{1\right\},\left\{2\right\},\left\{3\right\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}$

Therefore, the power set of A, $P\left(A\right)=\left\{\right\{\},\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\left\}\right\}$

Hence, the number of elements of the power set of A is 8.