Question

Let R be the relation over the set of straight lines of a plane, such that $l_{1}R{l}_2\iff l_1\pm l_2$ . Then, R is

• A. symmetric
• B. reflexive
• C. transitive
• D. an equivalence relation

Answer 1

The correct option is A symmetric

$l_{1}R{l}_1\Rightarrow l_1$ is not perpendicular to $l_1$
($\therefore$ R is not reflexive)
$l_{1}R{l}_2\Rightarrow l_1\pm l_2$
$\Rightarrow l_{2}R{l}_1\Rightarrow l_{2}R{l}_1$ , Hence, R is symmetric.
$l_{1}R{l}_2$ and $l_{2}R{l}_3\text{/}\Rightarrow l_{1}R{l}_3$ .($\therefore$ R is not transitive)