Q. 95.0( 1 Vote )

# Mark the tick against the correct answer in the following:Let S be the set of all real numbers and let R be a relation on S defined by a R b ⇔ |a| ≤ b. Then, R isA. reflexive but neither symmetric nor transitiveB. symmetric but neither reflexive nor transitiveC. transitive but neither reflexive nor symmetricD. none of these

According to the question ,

Given set S = {…….,-2,-1,0,1,2 …..}

And R = {(a, b) : a,b S and |a| ≤ b }

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

Consider , (a,a)

|a| ≤ a and which is not always true.

Ex_if a=-2

|-2| ≤ -2 2 ≤ -2 which is false.

Therefore , R is not reflexive ……. (1)

Check for symmetric

a R b |a| ≤ b

b R a |b| ≤ a

Both cannot be true.

Ex _ If a=-2 and b=-1

2 -1 is false and 1 -2 which is also false.

Therefore , R is not symmetric ……. (2)

Check for transitive

a R b |a| ≤ b

b R c |b| ≤ c

|a| ≤ c

Ex _a=-5 , b= 7 and c=9

5 ≤ 7 , 7 ≤ 9 and hence 5 ≤ 9

Therefore , R is transitive ……. (3)

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

Correct option will be (C)

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 current38 mins  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 