Absorption Laws (Set Theory)

Theorem

These two results together are known as the Absorption Laws, corresponding to the equivalent results in logic.

Union with Intersection

$S \cup \paren {S \cap T} = S$

Intersection with Union

$S \cap \paren {S \cup T} = S$

Corollary

$S \cup \paren {S \cap T} = S \cap \paren {S \cup T}$