Consider the relation R in the set Z of integers which is given by R = {(a, b) : 2 divides a - b}. Choose the correct option for the relation R:

Equivalence relation

The correct answer is Option (4) - Equivalence relation

for every $a∈z$

$a-a=0$ (divisible by z)

$⇒(a,a)∈R$ (Reflexive)

$(a,b)∈R$ ⇒ $a - b$ divisible by z ⇒ $b - a$ divisible by z

$⇒(b,a)∈R$ (Symmetric)

$(a,b)∈R,(b,c)∈R$

$a - b$ divisible by z, $b - c$ divisible by z

$a - b + b - c$ divisible by z

$⇒(a,c)∈R$ (Transitive)

⇒ R is equivalence Relation