Absorption Laws (Set Theory)/Corollary

From ProofWiki
Jump to navigation Jump to search

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
\(\ds \) \(\leadstoandfrom\) \(\ds S \cap \paren {S \cup T}\) Union is Idempotent

$\blacksquare$