Question

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 $R$ if $l_1$ is parallel to $l_2$. Then the relation $R$ is-

• A. Reflexive
• B. Symmetric
• C. Transitive
• D. Equivalence

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Reflexive
B Symmetric
C Transitive
D Equivalence

$l_{1}R{l}_1\Rightarrow l_1$ is parallel to itself. Reflexive

$l_{1}R{l}_2\Rightarrow l_{2}R{l}_1$ which is true. Symmetric

$l_{1}R{l}_2$ and $l_{2}R{l}_3\Rightarrow l_{1}R{l}_3$ which is true. Transitive. Hence all options are correct.