Hello,

I need to prove: when R is antisymmetric, then R inverse is antisymmetric. Can someone tell me whether I am correct or wrong?

Let R be antisymmetric, therefore $\displaystyle (a,b), (b,a) \in R$ where $\displaystyle a = b$. This gives us an inverse function which is $\displaystyle (b,a), (a,b) \in R^{-1}$ but because it is impossible to get $\displaystyle a \neq b$ when $\displaystyle a = b$ (in R), therefore $\displaystyle R^{-1}$ is antisymmetric.

Is this correct? I have the feeling that this is wrong... (If this is wrong can someone give me a counterexample?

Thanks for everything!