# Absorption Laws (Set Theory)/Union with Intersection/Proof 1

## Theorem

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

## Proof

 $\displaystyle$  $\displaystyle \paren {S \cap T} \subseteq S$ Intersection is Subset $\displaystyle$ $\leadsto$ $\displaystyle S \cup \paren {S \cap T} = S$ Union with Superset is Superset‎

$\blacksquare$