First slide

Relations XII

Question

Let L be the set of all straight lines in the Euclidean plane. Two lines l₁ and l₂ are said to be related by the relation R iff,l₁ is parallel to l₂. Then, the relation R is

Moderate

A

reflexive
B

transitive
C

symmetric
D

equivalence

Solution

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 l₁ is parallel to l₂, then l₂, is parallel to l₁.
R is symmetric relation. $[l_{1}, l_{2} \in L]$
let $l_{1}, l_{2}, l_{3} \in L$
l₁ is parallel to l₂, then l₂, is parallel to l₃.

Then, l₁, is parallel to l₃
R is transitive relation.
So, R is equivalence relation.

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