Power Set

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Formal Definition

The power set of any set $A$, written $\mathscr{P}(A)$, is the collection of all subsets of $A$, including $\emptyset$ and $A$ itself.

Informal Definition

Every possible subset created by the set including the set itself and the empty set.


If $A = \{a,b,c\}$, then $\mathscr{P}(A) = \{\emptyset,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\}$.


If $A = \{a,b,c\}$, then $\mathscr{P}(A)$ does not equal $\{\emptyset,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\}\}$ because it doesn't include the set $\{a,b,c\}$.

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