transitive relation

May 2014
2
0
Japan
Hello everyone!
I couldn't find more appropriate sub forum for that question so of it doesn't fit here I apology.
Transitive relation must be symmetric or antisymmetric? If so, how do I prove that? thanks! ;)
 
Apr 2014
320
156
Greater London, England, UK
Let $A=\{1,2,3\}$.

The relation $R_1=\{(1,2),\,(2,3),\,(1,3)\}$ on $A$ is transitive but not symmetric. ($1\,R_1\,2$ but $2\,\not{R_1}\,1$.)

The relation $R_2=\{(1,1),\,(1,2),\,(2,1)\}$ on $A$ is transitive but not antisymmetric. ($1\,R_2\,2$ and $2\,R_2\,1$ but $1\ne2$.)
 
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