First slide

Relations XII

Question

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

Moderate

A

reflexive
B

symmetric
C

transitive
D

an equivalence relation

Solution

$L_{1}$ is not $⊥ L_{1}$ , so $R$ is not reflexive
$L_{1} ⊥ L_{2} \Rightarrow L_{2} ⊥ L_{1} \Rightarrow R$ is symmetric.
$L_{1} ⊥ L_{2} a n d L_{2} ⊥ L_{3} \Rightarrow L_{1} ∥ L_{3} \Rightarrow R$ is not transitive.

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