Absorption Laws (Set Theory)/Union with Intersection

Theorem

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

Proof 1
$$ $$

Proof 2
$$ $$ $$

Comment
$$S \cup \left ({S \cap T}\right)$$ is also equal to $$S \cap \left ({S \cup T}\right)$$:

$$ $$ $$

See Intersection with Union.

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