Q. 55.0( 2 Votes )

Mark the tick against the correct answer in the following:

Let S be the set of all straight lines in a plane. Let R be a relation on S defined by a R b a || b. Then, R is

A. reflexive and symmetric but not transitive

B. reflexive and transitive but not symmetric

C. symmetric and transitive but not reflexive

D. an equivalence relation

Answer :

According to the question ,


Given set S = {x, y, z}


And R = {(x, x), (y, y), (z, z)}


Formula


For a relation R in set A


Reflexive


The relation is reflexive if (a , a) R for every a A


Symmetric


The relation is Symmetric if (a , b) R , then (b , a) R


Transitive


Relation is Transitive if (a , b) R & (b , c) R , then (a , c) R


Equivalence


If the relation is reflexive , symmetric and transitive , it is an equivalence relation.


Check for reflexive


Since , (x,x) R , (y,y) R , (z,z) R


Therefore , R is reflexive ……. (1)


Check for symmetric


Since , (x,x) R and (x,x) R


(y,y) R and (y,y) R


(z,z) R and (z,z) R


Therefore , R is symmetric ……. (2)


Check for transitive


Here , (x,x) R and (y,y) R and (z,z) R


Therefore , R is transitive ……. (3)


Now , according to the equations (1) , (2) , (3)


Correct option will be (D)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functional Equations - JEE with ease48 mins
Drift velocity & its relation with currentFREE Class
Relation between electric field and potential34 mins
Relation between Electric field & Potential45 mins
Interactive Quiz on Drift velocity & its relation with currentFREE Class
Interactive quiz on Relation between electric field and potential43 mins
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
view all courses