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  • Please help! - Sets, Relations and Functions - JEE Main-4

Let R be a relation over the set NxN and it is defined by (a,b)R(c,d)\Rightarrowa+d=b+c.Then R is

  • Option 1)

    Reflexive only

  • Option 2)

    Symmetric only

  • Option 3)

    Transitive only

  • Option 4)

    An equivalence relation

 

Answers (1)

best_answer

As we learnt

 

Equivalence relation -

 

Any relation which is reflexive, symmetric and transitive is called an equivalence relation

-

 

 We have (a,b)R(a,b) \forall(a,b)\inNxN.

Hence it is reflexive.

R is symmetric since (a,b)R(c,d)\Rightarrowa+d=b+c..........(i)

(c,d)R(e,f)\Rightarrowc+f=d+e............................(ii)

Thus  (a,b)R(e,f) is also true.

Since a+c+d+f=b+c+d+e (Add i and ii)

a+f=b+e

 


Option 1)

Reflexive only

Option 2)

Symmetric only

Option 3)

Transitive only

Option 4)

An equivalence relation

Posted by

Himanshu

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