Chapter P.1, Problem 11E

For the sets gives in Exercise 9, is there a “distributive relationship for union with respect with respect in intersection”? That is does

$A\cup \left(B\cap C\right)=\left(A\cup B\right)\cap (A\cup C)$?

$A=\left\{1, 2, 3, 4\right\}$, $B=\left\{2, 4, 6, 8\right\}$, and $C=\left\{1, 3, 5, 7, 9\right\}$.