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For the set S = {3, 4, 6}, which of the following relations on S is transitive but NOT reflexive?

1. R = {(3, 4), (4, 6), (3, 6)}
2. R = {(1, 2), (1, 3), (1, 4)}
3. R = {(3, 3), (4, 4), (6, 6)}
4. R = {(3, 4), (4, 3)}

Correct answer: R = {(3, 4), (4, 6), (3, 6)}

Solution

R = {(3,4),(4,6),(3,6)} is transitive (the only chain 3->4->6 has 3->6 present) and lacks all (a,a) pairs, so it is not reflexive.

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