Question

Let R be the relation over the set of all straight lines in a plane such that

$l_{1}R{l}_2\iff l_1\perp l_2$. Then, R is

• A. Symmetric
• B. Reflexive
• C. Transitive
• D. An equivalence

Answer 1

The correct option is A

Symmetric

Clearly R is not a reflexive relation, because a line cannot be perpendicular to itself.

Let $l_{1}R{l}_2$, Then

$l_{1}R{l}_2\Rightarrow l_1\perp l_2$

$\Rightarrow l_2\perp l_1$

$\Rightarrow l_{2}R{l}_1$

$\therefore$ R is a symmetric relation.

R is not a transitive relation, because if

$l_1\perp l_2$ And $l_2\perp l_1$, then $l_1$ may be parallel to $l_2$