What is the reflexive closure of $\{(a,b)~|~ a\neq b\}$?

Question

Let $R$ be a relation $\{(a,b)~|~ a\neq b\}$ on the set of integers. What is the reflexive closure of $R$?

Please help me. Solving the details please. Thanks.

Answer 1

The reflexive closure is all the elements that are already in the relation plus the ones that are needed to make the new relation reflexive. Hence, the reflexive closure is given by: $$R \cup \{(a,b) \, | \, a=b\}=\Bbb{Z} \times \Bbb{Z}.$$