Question

Let $A=\{x:x\in N\},B=\{x:x=2n,n\in N\},$

$C=\{x:x=2n-1,n\in N\}and$

$D=\{x:xisaprimenaturalnumber\}.$ Find.

(v) $(B\cap D)$

Answer 1

Given, $A=\{x:x\in N\},B=\{x:x=2n,n\in N\},$

$C=\{x:x=2n-1,n\in N\}and$

$D=\{x:xisaprimenaturalnumber\}.$
So, $A=$ set of natural numbers $=\{1,2,3,4,...\}$
$B=$ set of even natural numbers $=\{2,4,6,8,...\}$
$C=$ Set of odd natural numbers $=\{1,3,5,7,...\}$
$D=$ set of all prime natural number $=\{1,2,3,5,7,11,....\}$
We know that $2$ is only number which is even and prime.
Hence, $(B\cap D)$ $=\left\{2\right\}$.