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

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Theorem

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


Proof

\(\displaystyle \) \(\) \(\displaystyle S \subseteq \paren {S \cup T}\) Set is Subset of Union
\(\displaystyle \) \(\leadsto\) \(\displaystyle S \cap \paren {S \cup T} = S\) Intersection with Subset is Subset‎

$\blacksquare$