Find if the given relation equivalence?

Question

Let $A=\{x \in \mathbb Z:1 \le x \le 7\}$ and $R= \{(a,b):\vert a-b\vert \text{ is multiple of 4}\}$ a relation defined on set $A$.

Is $R$ an equivalence relation? What are all ordered pairs of $R$?

Answer 1

Where's your attempt?

$$R = \{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(1,5),(5,1),(2,6),(6,2),(3,7),(7,3)\} $$

Yes this relation is equivalence .

Answer 2

$$R=\left \{ (1,1),(2,2),(3,3),...,(1,5),(5,1),(2,6),(6,2),(3,7),(7,3) \right \}$$ R is reflexive ${\color{Red} {(1,1),...(7,7)}} $

R is symmetric $(1,5)\Leftrightarrow (5,1)$ ,...

R is transitive if you check

so it is equivalence relation