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X x X = { (a,a), (b,b), (c,c) }

{ (a,b), (b,a), (a,c), (c,a) }

{ (b,c), (c,b) }

1. Symmetric but not reflexive or transitive:

R = { (a,b), (b,a), (a,a), (b,c), (c,b) }

How come this is right? Isn't aRb, bRa imply aRa? isn't that transitive? is it because (b,c,), (c,b) is there but not (b,b) the reason why R is not transitive?

I ask because the 2nd question is confusing. Here it is:

2. Symmetric and transitive but not reflexive:

R= { (a,a), (a,b), (b,a), (b,b) }

See how aRb, bRa implies aRa so therefore it's transitive? How come it doesn't hold for the 1st question??

Thank you for any help.