Question

If $A=\left\{x:x\text{is a perfect square},x<50,x\in N\right\}$
$B=\left\{x:x=8m+1,\text{where}m\in W,x<50,x\in N\right\}$, then find $A\cap B$ and display it with Venn diagram.

Answer 1

Given $A=\{x:\text{x is a perfect square},x<50,x\in N\}$
$\Rightarrow A=\{1^2,2^2,3^3,4^2,5^2,6^2,7^2\}$
$\therefore A=\{1,4,9,16,25,36,49\}$

$B=\{x:x=8m+1,\text{where}m\in W,x<50,x\in N\}$
Since, $m$ is a whole number, so $m=0,1,2,3,.....$
for $m=0$ then $x=8\left(0\right)+1$
$\Rightarrow x=0+1$
$\therefore x=1<50$
so, $x=1$ belongs to set $B$
Similar way continuing for remaining values of $m$, we get $B=\{1,9,17,25,33,41,49\}$

Therefore,

$A\cap B=\{1,9,25,49\}$
Venn Diagram: