If is reflexive, then for all . If is one to one, then and implies that is, necessarily . This means that is the equality relation on (equivalence relation).
Lets say a set A has seven elements . Can a relation on A be 1-1, reflexive, but not symmetric?
I say no its impossible cause in order to be not symmetric and reflexive we would have to use an element in the domain more than once and that would not make it 1-1.
What do you think?