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

Theorem

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

Proof

\(\ds \)

\(\)

\(\ds \paren {S \cap T} \subseteq S\)

Intersection is Subset

\(\ds \)

\(\leadsto\)

\(\ds S \cup \paren {S \cap T} = S\)

Union with Superset is Superset‎

$\blacksquare$