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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, , denoted . 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 AX which is the identity on A.

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