Question

If $A=\{x\in W$ : $5<x<10\},B=\{3,4,5,6,7\}$ and $C=\{x=2n;n\in N$ and $n\le 4\}$, Find : $(A\cap B)\cup (A\cap C)$

Answer 1

$A=$ { $6,7,8,9$ } as $x$ is greater than $5$ but less than $10.$
$B=\{3,4,5,6,7\}$
And $C=$ { $2,4,6,8$ } as $x$ is multiple of $2$ with numbers $1$ to $4.$
Intersection of two sets has the elements common in both the sets
So, $A\cap B=$ { $6,7$ }
And $A\cap C=$ { $6,8$ }
Union of two sets has all the elements of both the sets
So , $(A\cap B)\cup (A\cap C)=$ { $6,7$ }$\cup$ { $6,8$ } $=$ { $6,7,8$ }