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# If A={x : x is a natural number},B={x : x is an even natural number},C={x : x is an odd natural number } and D={x : x is a prime number },Find (v) $B\cap D$

$\begin{array}{1 1}(A)\;\{1,2,3,4,5...\}&(B)\;\{2,4,6,8....\}\\(C)\;\{2,3,5,7,11....\}&(D)\;\{2\}\end{array}$

$B=\{2,4,6....\}$
$D=\{2,3,5,7....\}$
Hence only one element 2 is common in both B & D
$\therefore B \cap D=\{2,4,6...\}\cap \{2,3,5,7.....\}$
$\Rightarrow \{2\}$
Hence (D) is the correct answer.