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# If $A=\{3,5,7,9,11\},B=\{7,9,11,13\},C=\{11,13,15\}$ and $D=\{15,17\}$.Find (x) $(A\cup D)\cap(B \cup C)$

$\begin{array}{1 1}(A)\;\{3,5,7,9,11,15,17\}&(B)\;\{15,17\}\\(C)\;\{7,9,11,15\}&(D)\;\{11,15\}\end{array}$

$A\cup D=\{3,5,7,9,11\}\cup \{15,17\}$
$\Rightarrow \{3,5,7,9,11,16,17\}$
$B\cup C=\{7,9,11,13,15\}$
$\therefore A\cup D)\cap (B\cup C)$
$\Rightarrow$ 11,15 are the only element present in $(A\cup D)$ and $(B\cup C)$
$\therefore (A\cup D)\cap (B\cup C)=\{11,15\}$
Hence (D) is the correct answer.