# 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 Subsetâ€Ž |

$\blacksquare$