Question

Let $X=\{n\in N:1\le n\le 50\}$. If $A=\{n\in X:n\text{is a multiple of 2}\}$ and $B=\{n\in X:n\text{is a multiple of 7}\}$, then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is

Answer 1

$X=\{x:1\le x\le 50,x\in N\}$
$A=\{x:x\text{is a multiple of 2}\}=\{2,4,6,8,\dots ,50\}$
$B=\{x:x\text{is a multiple of 7}\}=\{7,14,21,\dots ,49\}$

Smallest subset of $X$ which contains elements of both $A$ and $B$ is a set with multiple of $2$ or $7$ less than $50$.
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$=25+7-3$
$=29$