Question

Let $A=Z$ and $B$ is the set of all multiple of $3$. Find $A\setminus B$ and $B\setminus A$

Answer 1

If we take out all multiples of $3$ from $Z$, the remaining numbers leave remainder either $1$ or $2$ when divided by $3$. Hence
$A\setminus B=\left\{x|xϵZ\text{and x leaves remainder}1or2\text{when divided by}3\right\}$
$=\{3a+1|aϵZ\}\cup \{3a+2|aϵZ\}$