Question

Let S be the relation defined by S = {(l₁, l₂) : l₁ is perpendicular to l₂} check whether the relation S is symmetric and transitive. 

Answer 1

Given relation, S = {(l₁, l₂) : l₁ is perpendicular to l₂}

Symmetric l₁ ⊥ l₂ ⇒ l₂ || l₁

(Two lines are perpendicular to each other)

Hence, S is symmetric.

Transitive:

Let l₁ ⊥ l₂ and l₂ ⊥ l₃ ⇒ l₁ || l₃

Thus, relation S is not transitive.