A={0,1,2,3} and there is a relation R={(0,0), (1,1),(2,0),(2,3),(2,2),(3,2),(3,3)}. Find out whether relation R is POSET or not?

Question

I've a doubt as to how this relation R is not anti-symmetric.

In the solution it's given that it's not anti-symmetric but according to me it's anti-symmetric. Since R2={(1,1),(0,0),(2,2),(3,3)}. Correct me if I am wrong.

Answer 1

Your relation contains both $(2,3)$ and $(3,2)$, but $2\ne 3$. Therefore it is not antisymmetric.

Note that "antisymmetric" is different from "not symmetric".