Set Difference Intersection with First Set is Set Difference/Proof 2
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Theorem
- $\paren {S \setminus T} \cap S = S \setminus T$
Proof
\(\ds \paren {S \setminus T} \cap S\) | \(=\) | \(\ds \paren {S \cap S} \setminus T\) | Intersection with Set Difference is Set Difference with Intersection | |||||||||||
\(\ds \) | \(=\) | \(\ds S \setminus T\) | Set Intersection is Idempotent |
$\blacksquare$