# Antisymmetric and irreflexive relation which is not asymmetric

Can anyone give me a counterexample for a relation $R\subset M\times M$ for the statement $$R\text{ antisymmetric} \wedge R\text{ not reflexive}\implies R\text{ asymmetric}$$

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I just got a question right now. What aboout $M=\{1,2\}$ and $R=\{(1,1),(1,2)\}$? –  Christian Ivicevic Dec 10 '12 at 13:42