# Absorption Laws (Set Theory)

## Theorem

These two results together are known as the Absorption Laws, corresponding to the equivalent results in logic.

### Union with Intersection

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

### Intersection with Union

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

### Corollary

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