Prove a relation is asymmetric if it is both anti-symmetric and irreflexive (anti-reflexsive).
I tried to go from the definitions of the relations:
Anti symmetric: $\forall x,y \, (xRy \land yRx \Rightarrow x=y )$
Irreflexsive: $\forall x\in A \ ,((x,x)\notin R) $
Assymetric: $\forall x,y \in A \,(xRy \Rightarrow \lnot yRx ) $
But it doesn't get me anywhere... I also tried to think about proof by contraposition but I can't seem to be able to connect the definitions.
Any help would be appreciated.