I am stuck with a question. It is stated below.
Let $R$ be a relation defined on the set of integers $\mathbb Z$ by the rule $aRb \iff |a-b|\leq 2$. Write the relation $R$ as a set.
Now there can be too many sets that satisfy this relation. How do I write the set $R$ representing the relation?
Given an integer $a$, the only integers $b$ which satisfy $|a-b|\le 2$ are $b=a-2,a-1,a,a+1,a+2$.
Thus the relation can be represented by the set $\{(n,n+k): n\in\mathbb{Z}, k\in\{-2,-1,0,1,2\}\}\subset\mathbb{Z}^2$.