Absorption Laws (Set Theory)/Corollary
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Theorem
- $S \cup \paren {S \cap T} = S \cap \paren {S \cup T}$
Proof
| \(\ds \) | \(\) | \(\ds S \cup \paren {S \cap T}\) | ||||||||||||
| \(\ds \) | \(\leadstoandfrom\) | \(\ds \paren {S \cup S} \cap \paren {S \cup T}\) | Union Distributes over Intersection | |||||||||||
| \(\ds \) | \(\leadstoandfrom\) | \(\ds S \cap \paren {S \cup T}\) | Set Union is Idempotent |
$\blacksquare$