Union is Idempotent

From ProofWiki
Jump to navigation Jump to search

Theorem

Set union is idempotent:

$S \cup S = S$


Proof

\(\ds x\) \(\in\) \(\ds S \cup S\)
\(\ds \leadstoandfrom \ \ \) \(\ds x \in S\) \(\lor\) \(\ds x \in S\) Definition of Set Union
\(\ds \leadstoandfrom \ \ \) \(\ds x\) \(\in\) \(\ds S\) Rule of Idempotence: Disjunction

$\blacksquare$


Also see


Sources