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

$\begin{array}{1 1}(A)\;\{3,5,7,9,11\}&(B)\;\{7,9,11,13\}\\(C)\;\{11,13,15\}&(D)\;\{7,9,11\}\end{array}$

Can you answer this question?

$A=\{3,5,7,9,11\}$
$B=\{7,9,11,13\}$
$C=\{11,13,15\}$
$A\cap B=\{3,5,7,9,11\}\cap \{7,9,11,13\}$
$\Rightarrow \{7,9,11\}$
$B\cup C=\{7,9,11,13\}\cup \{11,13,15\}$
$\Rightarrow \{7,9,11,13,15\}$
$\therefore (A\cap B)\cap (B\cup C)=\{7,9,11\} \cap \{7,9,11,13,15\}$
Here 7,9,11 are the only common elements in $(A\cap B)$ & $(B\cup C)$
$\therefore (A\cap B)\cap (B\cup C)=\{7,9,11\}$
Hence (D) is the correct answer.
answered May 27, 2014