I will upvote as soon as I can!

This is coded in Python.

Your second function is called "anti-symmetric". Its input is a relation (dictionary) R. Its output is a Boolean value. If R is an anti-symmetric relation, then the output is "True". The output is "False" otherwise. Note that it is not enough for the relation not to be symmetric. It has to satisfy the property that if a Rb and bra, then a=b