I would expect students to do the following.
If then .
So much of what you have done is correct, but not the starting place.
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 where . This gives us an inverse function which is but because it is impossible to get when (in R), therefore 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!
I disagree a bit, I see it as follow: R antisymmetric -> R inverse is antisymmetric. But starting from the conclusion, doesn't seem right to me, I think you should start from the assumption that R is antisymmetric and not from the assumption that R inverse is already antisymmetric.