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Let S denote the collection of all lines in a plane. Define a relation R on S by aRb if and only if line a is perpendicular to line b. Then R is:

1. reflexive but neither symmetric nor transitive
2. symmetric but neither reflexive nor transitive
3. transitive but neither reflexive nor symmetric
4. an equivalence relation

Correct answer: symmetric but neither reflexive nor transitive

Solution

A line is not perpendicular to itself (not reflexive); a⊥b implies b⊥a (symmetric); a⊥b and b⊥c make a parallel to c, not perpendicular (not transitive). So R is symmetric but neither reflexive nor transitive.

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