The relation R on set A={1, 2, 3, 4, 5}, given by R={(a, b) : |A-b| is even} is :

Equivalence

The correct answer is Option (1) → Equivalence

$A=\{1, 2, 3, 4, 5\}$

$R=|a-b|$ is even

→ for $∀a∈A$  $|a-a|=0$ (always even)

so $(a,a)∈R$ ⇒ Reflexive relation

→ for $(a,b)∈R$

$|(a-b)|$= Even

so $|a-b|=|b-a|$ is even

so $(b,a)∈R$ ⇒ Symmetric relation

→ for $(a,b)∈R,(b,c)∈R$

if (a, b) both are odd ⇒ b, c both are odd and if a, b are both even ⇒ b, c both are even

$⇒ |a - c|$ is even so $(a,c)∈R$ ⇒ Transitive relation

⇒ Equivalence relation