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

Theorem

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

Proof

\(\ds \)

\(\)

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

Set is Subset of Union

\(\ds \)

\(\leadsto\)

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

Intersection with Subset is Subset‎

$\blacksquare$