The power set

#power set#subsets#cardinality

Statement

Let $A=\{1,2,3\}$ . List all elements of $\mathcal{P}(A)$ and give its cardinality.

Hint

A set with $n$ elements has $2^n$ subsets.

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List.
$\mathcal{P}(A)=\{\emptyset,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}.$

Cardinality. $|\mathcal{P}(A)|=2^3=8$ .

Conclusion. $\mathcal{P}(A)$ has $8$ elements.