# Absorption Laws (Set Theory)/Corollary

$S \cup \left ({S \cap T}\right) = S \cap \left ({S \cup T}\right)$
 $\displaystyle$  $\displaystyle S \cup \left ({S \cap T}\right)$ $\displaystyle$ $\iff$ $\displaystyle \left ({S \cup S}\right) \cap \left ({S \cup T}\right)$ Union Distributes over Intersection $\displaystyle$ $\iff$ $\displaystyle S \cap \left ({S \cup T}\right)$ Union is Idempotent
$\blacksquare$