Answer :

Let R = {(x,y): x is greater than y x,y N } be a relation defined on N.


Now,


We observe that, any element x N cannot be greater than itself.


(x,x) R x N


R is not reflexive.


Let (x,y) R x, y N


x is greater than y


But y cannot be greater than x if x is greater than y.


(y,x) R


For e.g., we observe that (5,2) R i.e 5 > 2 but 2 5 (2,5) R


R is not symmetric


Let (x,y) R and (y,z) R x, y,z N


x > y and y > z


x > z


(x,z) R


For e.g., we observe that


(5,4) R 5 > 4 and (4,3) R 4 > 3


And we know that 5 > 3 (5,3) R


R is transitive.


Thus, R is transitive but not reflexive not symmetric.


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 :

Fill in theMathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

Let A = {1, 2, 3}Mathematics - Exemplar

Show that the relMathematics - Board Papers

Let N denote the Mathematics - Board Papers