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

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## Theorem

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

## Proof

\(\displaystyle \) | \(\) | \(\displaystyle \paren {S \cap T} \subseteq S\) | Intersection is Subset | ||||||||||

\(\displaystyle \) | \(\leadsto\) | \(\displaystyle S \cup \paren {S \cap T} = S\) | Union with Superset is Supersetâ€Ž |

$\blacksquare$