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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find <a name="_HlRS Aggarwal - Mathematics

Let A be the set RS Aggarwal - Mathematics

If R is a binary RS Aggarwal - Mathematics

Let f : R <span lRS Aggarwal - Mathematics

Let R = (x, y) : RS Aggarwal - Mathematics

Mark the correct RD Sharma - Mathematics

If R is a RD Sharma - Mathematics

What is an equivaRS Aggarwal - Mathematics

Let R = {(a, b) :RS Aggarwal - Mathematics

Mark the correct RD Sharma - Mathematics