In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide. The relationship of one set being a subset of another is called inclusion.
If A and B are sets and every element of A is also an element of B, then:
If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B not contained in A), then
Some authors use the symbols ⊂ and ⊃ to indicate "subset" and "superset" respectively, instead of the symbols ⊆ and ⊇, but with the same meaning. So for example, for these authors, it is true of every set A that A ⊂ A.
Other authors prefer to use the symbols ⊂ and ⊃ to indicate proper subset and superset, respectively, in place of