Let L be the set of all straight lines in the Euclidean plane. Two lin – InterviewSolution

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1.	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 iff `l_(1)` is parallel to `l_(2)`. Then, the relation R is notA. reflexiveB. symmetricC. transitiveD. equivalence
Answer» Correct Answer - 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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