# Absorption Laws (Set Theory)/Intersection with Union/Proof 1

Jump to navigation
Jump to search

## Theorem

- $S \cap \paren {S \cup T} = S$

## Proof

\(\displaystyle \) | \(\) | \(\displaystyle S \subseteq \paren {S \cup T}\) | Set is Subset of Union | ||||||||||

\(\displaystyle \) | \(\leadsto\) | \(\displaystyle S \cap \paren {S \cup T} = S\) | Intersection with Subset is Subset |

$\blacksquare$