R and S are relations on A.

If R and S are asymmetric, then are asymmetric.

Can this been done by using generic nxn matrices and showing and where "and" is the the Boolean meet symbol?

Printable View

- Nov 6th 2010, 11:55 AMdwsmithSymmetry proof
R and S are relations on A.

If R and S are asymmetric, then are asymmetric.

Can this been done by using generic nxn matrices and showing and where "and" is the the Boolean meet symbol? - Nov 6th 2010, 12:49 PMDefunkt
I don't know what the boolean meet symbol is but you can try the following:

To prove is anti-symmetric, assume and and continue using the fact that both R and S are anti-symmetric. - Nov 7th 2010, 01:36 PMemakarov
"Asymmetric" is not the same as "antisymmetric". I believe, the former means . However, the same proof idea works. In fact, if at least one of R and S is asymmetric, then is asymmetric.

- Nov 7th 2010, 02:33 PMDefunkt
Oh, I was sure I read anti-symmetric; my bad then.

I'm not sure about the asymmetric part, though -- I've seen some books define an asymmetric relation as one that is simply not symmetric, so OP should clarify (the same idea will work for all cases)