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Let R be the relation over the set of al...

Let `R` be the relation over the set of all straight lines in a plane such that `l_1\ R\ l_2hArrl_1_|_l_2`. Then, `R` is (a) symmetric (b) reflexive (c) transitive (d) an equivalence relation

A

symmetric

B

reflexive

C

transitive

D

an equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, R is not a reflexive relation, because a line cannot be perpendicular to itself.
Let `l_(1) R l_(2)`. Then,
`l_(1) R l_(2)implies l_(1) _|_ l_(2) implies l_(2)_|_l_(1)implies l_(2)Rl_(1)`
`therefore` R is a symmetric relation.
R is not a transitive relation, because if
`l_(1) _|_ l_(2) and l_(2) _|_l_(3)`, then `l_(1)` may be parallel to `l_(3)`.
Hence, option (a) is correct.
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