Mark the correct alternative in the following question: Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m ∈ L. Then, R is ______________ .

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KollegeApply · Accepted Answer

We have, R = {(l, m) : l is perpendicular to m; l, m ∈ L} As, l is not perpencular to l ⇒ (l, l) ∉ R So, R is not reflexive relation Let (l, m) ∈ R ⇒ l is perpendicular to m ⇒ m is also perpendicular to l ⇒ (m, l) ∈ R So, R is symmetric relation Let (l, m) ∈ R and (m, n) ∈ R ⇒ l is perpendicular to m and m is perpendicular to n ⇒ l is parallel to n (Lines perpendicular to same line are parallel) ⇒ (m, l) ∉ R So, R is not transitive relation Hence, R is symmetric.

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