# Symmetry proof

• November 6th 2010, 11:55 AM
dwsmith
Symmetry proof
R and S are relations on A.

If R and S are asymmetric, then $R \cap S$ are asymmetric.

Can this been done by using generic nxn matrices and showing $M_R$ and $M_S$ where "and" is the the Boolean meet symbol?
• November 6th 2010, 12:49 PM
Defunkt
I don't know what the boolean meet symbol is but you can try the following:

To prove $R \cap S$ is anti-symmetric, assume $(x,y) \in R \cap S$ and $(y,x) \in R \cap S$ and continue using the fact that both R and S are anti-symmetric.
• November 7th 2010, 12:36 PM
emakarov
"Asymmetric" is not the same as "antisymmetric". I believe, the former means $\forall x,y.\,(x,y)\in R\Rightarrow (y,x)\notin R$. However, the same proof idea works. In fact, if at least one of R and S is asymmetric, then $R\cap S$ is asymmetric.
• November 7th 2010, 01:33 PM
Defunkt