Question

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

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

$C=\{x:x=2n-1,n\in N\}and$
$D=\{x:x\text{is a prime natural number}\}$. Find.

(i) $(A\cap B)$

Answer 1

Given, $A=\{x:x\in N\},$ $B=\{x:x=2n,n\in N\},$
$C=\{x:x=2n-1,n\in N\}and$
$D=\{x:x\text{is a prime natural number}}.$

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 $=\{1,2,3,5,7,11,.....\}$
Since, $(A\cap B)$. Therefore,
$(A\cap B)$$=\{1,2,3,4,....\}$ $\cap$ $\{2,4,6,8,....\}$
$(A\cap B)$ $=\{2,4,6,8,.....\}$
Hence, $(A\cap B)$ $=\{2,4,6,8,....\}=B.$