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. Reflexive but not symmetric
• C. reflexive but not transitive
• D. transitive

Answer 1

Answer: (A), (D)

transitive

$l_{1}R{l}_1\text{as}{l}_1$ is parallel to itself, So it is reflexive.
$l_{1}R{l}_2\Rightarrow l_{2}R{l}_1,$ which is true, so it is symmetric.
$l_{1}R{l}_2$ and $l_{2}R{l}_3$ $\Rightarrow l_{1}R{l}_3,$ which is true, so it is transitive.