Question

Let $A=\{3,6,9,12,15,...\}$ and $B=\{2,4,6,8,10,...\}$. Find $A\cup B$ and represent it in set builder method

Answer 1

Observe that $A$ is the set of natural numbers which are multiples of $3$. Similarly, $B$ is the set of natural numbers which are multiples of $2$. Hence their union is the set of natural numbers which are either multiples of $3$ or multiples of $2$. Thus
$A\cup B=\{x:xϵN,x=2k\text{for some}kϵNorx=3k\text{for some}kϵN\}$.