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On the set I = {4, 5}, which of the following relations is symmetric and transitive but not reflexive?

1. R = {(4,4), (5,4), (5,5)}
2. R = {(4,4), (5,5)}
3. R = {(4,5), (5,4)}
4. R = {(4,5), (5,4), (4,4)}

Correct answer: R = {(4,5), (5,4)}

Solution

R = {(4,5),(5,4)} lacks (4,4) and (5,5) so it is not reflexive, while being symmetric; it is the intended non-reflexive symmetric relation.

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