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Question

Let R be the relation over the set of all straight lines in a plane such that l1 R l2 ⇔ l 1⊥ l2. Then, R is
(a) symmetric
(b) reflexive
(c) transitive
(d) an equivalence relation

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Solution

(a) symmetric

A = Set of all straight lines in the plane

R=l1, l2 : l1, l2A : l1l2Reflexivity: l1 is not l1l1, l1RSo, R is not reflexive on A.Symmetry: Let l1, l2Rl1l2l2l1l2, l1RSo, R is symmetric on A.Transitivity: Let l1, l2R, l2, l3Rl1 l2 and l2 l3But l1 is not l3l1, l3RSo, R is not transitive on A.

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