Intersection Absorbs Union/Proof 2
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Theorem
- $S \cap \paren {S \cup T} = S$
Proof
| \(\ds x\) | \(\in\) | \(\ds S \cap \paren {S \cup T}\) | ||||||||||||
| \(\ds \leadstoandfrom \ \ \) | \(\ds x\) | \(\in\) | \(\ds S \land \paren {x \in S \lor x \in T}\) | Definition of Set Intersection and Definition of Set Union | ||||||||||
| \(\ds \leadstoandfrom \ \ \) | \(\ds x\) | \(\in\) | \(\ds S\) | Conjunction Absorbs Disjunction |
$\blacksquare$