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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 (iv) $B\cap C$

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

$B=\{2,4,6....\}$
$C=\{1,3,5....\}$
Hence there is no common elements in both B & C
$\therefore B \cap C=\{2,4,6....\}\cap \{1,3,5....\}$
$\Rightarrow \phi$
Hence (A) is the correct answer.