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

Question

Let L denote the set of all straight lines in a plane. Let a relation R be defined by α R β Leftrightarrow α perp β, α, β ∈ L. Then R is (A) Reflexive (B) Symmetric (C) Transitive (D) None of these

Tardigrade Admin · Accepted Answer

Here α R β Leftrightarrow α perp β ∴ α perp β Leftrightarrow β perp α Hence, R is symmetric. But, α perp α and if α perp β β perp &gamma; ⇒ α perp &gamma;

Q. Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $α Rβ \Leftrightarrow α ⊥ β, α, β \in L$ . Then $R$ is

Reflexive

Symmetric

Transitive

None of these

Here $α Rβ \Leftrightarrow α ⊥ β$
$∴ α ⊥ β \Leftrightarrow β ⊥ α$
Hence, R is symmetric.
But, $α ⊥ α$ and if $α ⊥ β & β ⊥ γ$
$\Rightarrow α ⊥ γ$

Q. 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. Then R is