Q. 64.0( 8 Votes )

Let R = {(a, b) :

Answer :

(i) Reflexivity: Let a є Z, a - a = 0 є Z which is also even.

Thus, (a, a) є R for all a є Z. Hence, it is reflexive

(ii) Symmetry: Let (a, b) є R

(a, b) є R è a - b is even

-(b - a) is even

(b - a) is even

(b, a) є R

Thus, it is symmetric

(iii) Transitivity: Let (a, b) є R and (b, c) є R

Then, (a – b) is even and (b – c) is even.

[(a - b) + (b - c)] is even

(a - c) is even.

Thus (a, c) є R.

Hence, it is transitive.

Since, the given relation possesses the properties of reflexivity, symmetry and transitivity, it is an equivalence relation.

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