# Absorption Laws (Set Theory)/Corollary

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## Theorem

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

## Proof

 $\ds$  $\ds S \cup \paren {S \cap T}$ $\ds$ $\leadstoandfrom$ $\ds \paren {S \cup S} \cap \paren {S \cup T}$ Union Distributes over Intersection $\ds$ $\leadstoandfrom$ $\ds S \cap \paren {S \cup T}$ Union is Idempotent

$\blacksquare$