Is there a relation that is irreflexive, anti-symmetric and not transitive? from the set $\{a, b, c, d\}$?
Of the one's I have tried, it at best is two of the three, but never all.

Consider the ordered pair, such that $\{(x,y)\,|\,x,y\in\{a,b,c,d\}\}$.  The following relation satisfies those conditions:
$$\{(a,b) ,(b,c), (c,d), (d,a)\}$$
Clearly, this relation is not reflexive since there is no ordered pair with same members i.e. $(x,x)$.  This relation is anti-symmetric since for instance, there is no ordered pair $(b,a)$.  This relation is also not transitive (which is left for you to work out).
