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

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

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Reflexive

Symmetric

Transitve

None of these

answer is B.

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Detailed Solution

$Here, α R β \Leftrightarrow α ⊥ β ∴ α ⊥ β \Leftrightarrow β ⊥ α$

Hence, R is symmetric

One line is not perpendicular to it self, so that R is not reflexive

Suppose (L,M), (M,N) are ordered pairs of R, it means L is perpendicular to M and M is perpendicular to N

it does not implies that L is perpendicular to N, so that (M, N) does not belongs to R

so that R is not transitive

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