## Simplifying Expressions Involving Unions and Intersections of Sets

The set distributively Laws state that for events
$A, \:, B, \: C$
:
$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$

$A \cap (B \cup C)=(A \cap B) \cup (A \cap C)$

We can use these laws to simplify many expressions involving unions and intersections. For example:
$(A \cup B) \cap A' =A' \cap (A \cup B)=(A' \cap A) \cup (A' \cap B)= \emptyset \cup (A \cap B)=A \cap B$

$(A \cap B) \cup (A' \cap B)=(B \cap A) \cup (B \cap A')=B \cap (A \cup A')=B \cap \mathcal{U} =B$