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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 _____________ .
Options
Symmetric
Reflexive
Transitive
an equivalence relation
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Solution
Symmetric
A = Set of all straight lines in the plane
R={( l1, l2) : l1, l2∈ A : l1 ⊥ l2}
Reflexivity: l1 is not ⊥ l1
⇒ (l1,l1) ∉ R
So, R is not reflexive on A.
Symmetry: Let (l1, l2) ∈ R
⇒l1⊥l2
⇒l2⊥l1
⇒(l2, l1) ∈ R
So, R is symmetric on A.
Transitivity: Let (l1, l2) ∈ R, (l2, l3) ∈ R
⇒ l1⊥ l2 and l2⊥ l3
But l1 is not ⊥ l3
⇒(l1, l3) ∉ R
So, R is not transitive on A.
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