Theorem: $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$ Proof: Let $x \in A \cap (B \cup C)$. Then $x \in A$ and $x \in B \cup C$. So $x \in A$ and ($x \in B$ or $x \in C$). If $x \in B$, then $x \in A \cap B$. If $x \in C$, then $x \in A \cap C$. Either way, $x \in (A \cap B) \cup (A \cap C)$. The reverse inclusion is similar. $\square$ Join Discord PreviousSet TheoryNextRelations and Functions