Let $X =\{ a,b,c,d\}$ be a set a of possible choices. Define a relation of preference $R$ which generates a rule of choice $C'$ such that it generates another relation $R'$ which is different from $R$ (or prove it's impossible).
I would be very obliged if someone could help me to sort it out. I suppose that non-existence of such a rule must be shown by contradiction but I have no idea how to do it nicely in mathematical terms.