Absorption Laws (Set Theory)/Intersection with Union

Theorem

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

Proof 1
$$ $$

Proof 2
$$ $$ $$

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

$$ $$ $$

See Union with Intersection.

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