Let L be set of all straight lines in Euclidean plane. Two lines {l₁} and {l₂} are said to be re

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1.Relation and Function

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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

A

Reflexive

B

Symmetric

C

Transitive

D

All of above

Solution

(d) Here ${l_1}R{l_2}$

${l_1}$ is parallel ${l_2}$ and also ${l_2}$ is parallel to ${l_1}$, so it is symmetric.

Clearly, it is also reflexive and transitive.

Hence it is equivalence relation.

Standard 12

Mathematics

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