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

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 . R is symmetric relation. [ l 1 , l 2 ∈ L ] let l 1 , l 2 , l 3 ∈ L l 1 is parallel to l 2 , then l 2 , is parallel to l 3 . Then, l 1 , is parallel to l 3 R is transitive relation. So, R is equivalence relation.

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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

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reflexive

equivalence

symmetric

transitive

answer is A, B, C, D.

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Detailed 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.