Union Absorbs Intersection/Proof 1
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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 |
$\blacksquare$