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Let L be the set of all straight lines i...

Let L be the set of all straight lines in the Euclidean plane. Two lines `l_(1)` and `l_(2)` are said to be related by the relation R if `l_(1)` is parallel to `l_(2)`. Then, relation R is not

A

reflexive

B

symmetric

C

transitive

D

none of the above

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Relation R on the set of all straight lines in the plane is of parallel line.
A line is parallel to itself. So, R is reflexive.
If `l_(1)` is parallel to `l_(2)`, then `l_(2)` is parallel to `l_(1)`.
`therefore` R is symmetric relation. `[l_(1), l_(2) in L]`
Let `l_(1), l_(2), l_(3) in L`
`l_(1)` is parallel to `l_(2)` and `l_(2)` is parallel to `l_(3)`.
Then, `l_(1)` is parallel to `l_(3)`
`therefore R` is transitive relation.
So, R is equivalence relation.
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