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Let L denote the set of all the straight lines in a plane. Let a relation R be defined by aR\beta \Rightarrow a\perp \beta ;a,\beta \epsilon L. Then R is

  • Option 1)

    Reflexive

  • Option 2)

    Symmetric

  • Option 3)

    Transitive

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt

 

TRANSITIVE RELATION -

 

A relation R in A is said to be transitive, if a R b and b R c ⇒ a R c ∀ a,b,c ∈ A

-

 

 Here,\alpha R\beta \Leftrightarrow \alpha \perp \beta \: \: \therefore \alpha \perp \beta \Leftrightarrow \beta \perp \alpha

Hence R is symmetric.

But it is not transitive.

 


Option 1)

Reflexive

Option 2)

Symmetric

Option 3)

Transitive

Option 4)

none of these

Posted by

Himanshu

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