Subset

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In set theory, a subset of a set X is a set A whose elements are all elements of X: that is, ${\displaystyle x\in A\Rightarrow x\in X}$, denoted ${\displaystyle A\subseteq X}$. The empty set Ø and X itself are always subsets of X. The containing set X is a superset of A. The relation between the subset and the superset is inclusion, and the inclusion map is the map from A → X which is the identity on A.

The power set of X is the set of all subsets of X.