Absorption Laws (Set Theory)

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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

$S \cup \left ({S \cap T}\right) = S \cap \left ({S \cup T}\right)$


Sources