The relation R on the set N × N defined by (a, b) R(c, d) ⇔ a + d = b + c ∀ (a, b), (c, d), ∈ N × N is ,where N is set of natural number :

Equivalence

The correct answer is Option (4) → Equivalence

(1) Reflexive

for every $(a, b)∈N×N,(a+b)=(b+a)$

(2) Symmetric

for every $(a,b)R(c,d)$,  $(a+b)=(c+d)$

$⇒(c+d)=(b+a)⇒(c,d)R(a,b)$

(3) Transitive

for every $(a,b)R(c,d),(c,d)R(e,f)$

$a+b=d+c,c+d=f+e$

$⇒a+b=f+e,⇒(a,b)R(e,f)$

⇒ Equivalence relation