R = {(a,b) is an element of A cross B with (b,a) an element of R inverse}

Proof:

If R is antisymmetric, then R inverse is antisymmetric

-if you can not prove this I must show a counterexample thanks

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- Mar 27th 2008, 04:16 PMteeplkylantisymmetric
R = {(a,b) is an element of A cross B with (b,a) an element of R inverse}

Proof:

If R is antisymmetric, then R inverse is antisymmetric

-if you can not prove this I must show a counterexample thanks - Mar 27th 2008, 06:07 PMThePerfectHacker
You need to show if R is antisymettric, meaning if a<=b and b<=a implies a=b. Then $\displaystyle R^{-1}$ has the same property. It should be clear how to do this by definition.

- Mar 27th 2008, 07:07 PMPlato
If $\displaystyle (x,y) \in R^{ - 1} \wedge (y,x) \in R^{ - 1} \quad \Rightarrow \quad (y,x) \in R \wedge (x,y) \in R.$

But we know that $\displaystyle R$ is antisymmetric so $\displaystyle x=y$.