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 number of elements in (B $\cup$ A) $\cap$ (B $\cup$ C)

Answer 1

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