Question

If $A=(5,6,7,8,9),B=\{x:3<x<8\text{and}x\in W\}$ and $C=\{x:x\le 5\text{and}x\in N\}$. Find number of elements in (A $\cup$ B) $\cup$ C.

Answer 1

From the given sets, we have

$B$ $=$ { $4,5,6,7$ } as $x$ is greater than $3$ but less than $8$

And $C$ $=$ { $1,2,3,4,5$ } as $x$ is a natural number less than equal to $5$.

Union of two sets has all the elements of both the sets
So, $A\cup B=$ { $4,5,6,7,8,9$ }

And, $(A\cup B)\cup C=$ { $4,5,6,7,8,9$ }$\cup$ { $1,2,3,4,5$ } $=$ { $1,2,3,4,5,6,7,8,9$ }

$n\left(\right(A\cup B)\cup C)=9$