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For the set A = {1, 2, 3}, which relation is symmetric but neither reflexive nor transitive?

1. R = {(1, 2), (1, 3), (1, 4)}
2. R = {(1, 2), (2, 1)}
3. R = {(1, 1), (2, 2), (3, 3)}
4. R = {(1, 1), (1, 2), (2, 3)}

Correct answer: R = {(1, 2), (2, 1)}

Solution

R = {(1,2),(2,1)} is symmetric, lacks (1,1) etc. (not reflexive), and has (1,2),(2,1) but not (1,1) (not transitive).

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