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## Homework Statement

Prove that if R is a symmetric relation on A, and Dom(R) = A, then R = the identity relation.

**2. The attempt at a solution**

My problem is... I don't believe the claim. At all. If A = {1, 2, 3} and R = {(1, 2), (2, 1), (3, 1), (1, 3)}, that satisfies the antecedent, and isn't the identity relation. Am I missing something? I can't exactly prove something I don't believe. Thanks for any help or explanations you can provide.

p.s. This book has been known to have typos eeeeeverywhere. Suggestions as to what they really meant (antisymmetric? that wouldn't even work I don't think) are appreciated as well.