Quick and easy question about anti-symmetrical property of relations

Question

I'm studying for final exams by doing past-years exams and comparing my answers to the solutions that are appended at the end of the document.

There is a problem that asks to list all the properties of a relation

R = {(a, b) : a/5 = b/5} a,b are integers

The prof's answers are that relation R is reflexive, symmetrical and transitive.

But isn't it also anti-symmetrical?

Thanks

Answer 1

Yes, you are correct. The relation $R$ is of course the same as the identity relation (since $\frac{a}{5}=\frac{b}{5}$ iff $a=b$), which is symmetrical and anti-symmetrical