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Let L be the set of all lines in a plane and let R be the relation on L given by R = {(L1, L2): L1 is perpendicular to L2}. Which of the following correctly describes R?

1. R is symmetric but neither reflexive nor transitive
2. R is reflexive, symmetric and transitive (an equivalence relation)
3. R is reflexive and symmetric but not transitive
4. R is transitive but neither reflexive nor symmetric

Correct answer: R is symmetric but neither reflexive nor transitive

Solution

Perpendicularity is symmetric (the relation is mutual) but not reflexive (no line is perpendicular to itself) and not transitive (two lines perpendicular to the same line are parallel, hence not perpendicular to each other).

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