Absorption Laws (Set Theory)/Corollary

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Theorem

$S \cup \left ({S \cap T}\right) = S \cap \left ({S \cup T}\right)$


Proof

\(\displaystyle \) \(\) \(\displaystyle S \cup \left ({S \cap T}\right)\)
\(\displaystyle \) \(\iff\) \(\displaystyle \left ({S \cup S}\right) \cap \left ({S \cup T}\right)\) Union Distributes over Intersection
\(\displaystyle \) \(\iff\) \(\displaystyle S \cap \left ({S \cup T}\right)\) Union is Idempotent

$\blacksquare$