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 relation

Answer 1

The correct option is A symmetric

For some lines $l_1,l_2$, We know that $l_1\perp l_2\leftrightarrow l_2\perp l_1$

So, given relation is symmetric .

For some lines $l_1,l_2,l_3$, We know that if $l_1\perp l_{2}and{l}_2\perp l_3$, then $l_1\parallel l_3$

So, given relation is not transitive .

For some line $l$, We know that it is never possible that $l\perp l$.

So, given relation is not reflexive .

Thus $A$ is correct answer .