Q.

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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a

reflexive

b

transitive

c

symmetric

d

equivalence

answer is A.

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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. [l1,l2∈L]let l1,l2,l3∈L l1 is parallel to l2, then l2, is parallel to l3.Then,  l1, is parallel to l3R 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