Question

$R$ is a relation over the set of integers and it is given by $(x,y)\in R\iff |x-y|\le 1$.Then $R$ is

• A. reflexive and transitive
• B. reflexive and symmetric
• C. symmetric and transitive
• D. an equivalence relation

Answer 1

The correct option is B reflexive and symmetric

$|x-x|\le 1$ is true.So the relation is reflexive.

If $|x-y|\le 1$ then $|y-x|\le 1$. So the relation is symmetric.

If $|x-y|\le 1,|y-z|\le 1$then we cant be sure that $|x-z|\le 1$.Hence it cannot be transitive.