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Math Help - Symmetry proof

  1. #1
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    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?
    Last edited by mr fantastic; November 6th 2010 at 12:59 PM. Reason: Fixed spacing problem.
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  2. #2
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    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.
    Last edited by mr fantastic; November 6th 2010 at 01:05 PM.
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  3. #3
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    "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.
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  4. #4
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    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)
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