Question

Let R be a relation on the set L of lines defined by l₁ R l₂ if l₁ is perpendicular to l₂, then relation R is ____________.

Options

• reflexive and symmetric

• symmetric and transitive

• equivalence relation

• symmetric

Answer 1

Let R be a relation on the set L of lines defined by l₁ R l₂ if l₁ is perpendicular to l₂, then relation R is symmetric.

Explanation:

not reflexive, as l₁ R l₂

⇒ I₁ ⊥ I₁ Not true

Symmetric, true as l₁ R l₂ ⇒ l₂R h

Transitive, false as l₁ R l₂, l₂ R l₃

⇒ l₁ || l₃ . l₁ R l₂.