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  • Please,please help me - Sets, Relations and Functions - JEE Main-6

Let R be a relation on the set R of all real numbers defined by aRb if \left | a-b \right |\leq 1. Then R is

  • Option 1)

    Reflexive and symmetric

  • Option 2)

    symmetric only

  • Option 3)

    Transitive

  • Option 4)

    Anti-symmetric only

 

Answers (1)

best_answer

As we learnt

 

SYMMETRIC RELATION -

 

A relation R in A is said to be symmetric, if a R b ⇒ b R a,∀ a,b ∈ A

-

 

 

\left | a-a \right |= 0<1\: \therefore aRa\: \forall \: a\in R

\therefore R is reflexive.

Also aRb\Rightarrow \left | a-b \right |\leq 1\Rightarrow \left | b-a \right |\leq 1\Rightarrow bRa


Option 1)

Reflexive and symmetric

Option 2)

symmetric only

Option 3)

Transitive

Option 4)

Anti-symmetric only

Posted by

Himanshu

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