# The relation ‘R’ in N × N such that (a, b) R (c, d) ⬄ a + d = b + c isA. reflexive but of symmetricB. reflexive and transitive but not symmetricC. an equivalence relationD. none of these

Check:

(a,b)R (a,b) R

a + b = b + a

hence R is reflexive.

Now,

(a, b) R (c, d) R

a + d = b + c

c + b = d + a

(c,d) R (a,b) R

R is symmetric

Now,

(a, b) R (c, d) R

a + d = b + c

(c,d) R (e,f) R

c + f = d + e

Now,

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

a + f = b + e

So (a,b) R (e,f)

R is transitive.

Hence R is an equivalence relation.

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