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Let $L$ be the set of all lines in a plane and $R$ be a relation on $L$ defined by $l_{1} R l_{2}$ if and only if $l_{1} ⊥ l_{2}$ then $R$ is

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reflexive

symmetric

transitive

an equivalence relation

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detailed solution

Correct option is B

L1 is not ⊥L1, so R is not reflexiveL1⊥L2⇒L2⊥L1⇒R is symmetric.L1⊥L2 and L2⊥L3⇒L1∥L3⇒R is not transitive.

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Let L be the set of all lines in a plane and R be a relation on L defined by l1R l2 if and only if l1⊥l2 then R is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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Let $L$ be the set of all lines in a plane and $R$ be a relation on $L$ defined by $l_{1} R l_{2}$ if and only if $l_{1} ⊥ l_{2}$ then $R$ is