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Question: Let L denote the set of all straight lines in a plane. Let a relation R be defined by \(\alpha R \be...

Let L denote the set of all straight lines in a plane. Let a relation R be defined by αRβ⇔α⊥β,α,β∈L\alpha R \beta \Leftrightarrow \alpha \perp \beta , \alpha , \beta \in L. Then R is

A

Reflexive

B

Symmetric

C

Transitive

D

None of these

Answer

Symmetric

Explanation

Solution

Here αRβ⇔α⊥β\alpha R \beta \Leftrightarrow \alpha \perp \beta ∴α⊥β⇔β⊥α\alpha \perp \beta \Leftrightarrow \beta \perp \alpha

Hence, R is symmetric.