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Math Help - Antisymetric and symmetric

  1. #1
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    Antisymetric and symmetric

    Can some1 explain to me what these means and how i can tell if a relation is symmetric or anti or both?

    Im reading the definition over and over for like 10x already and i jsut don't understand.

    The example they gave in the book is...

    set A {1 2 3 4 }

    R = { (2,1), (3,1), (3,2), (4,1), (4,2), (4,3) } is antisymmetric...But why??

    What is (a,b) and (b,a) and a=b? i dont understand?
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  2. #2
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    Quote Originally Posted by smoothi963 View Post

    R = { (2,1), (3,1), (3,2), (4,1), (4,2), (4,3) } is antisymmetric...But why??

    What is (a,b) and (b,a) and a=b? i dont understand?
    Meaning,
    If (x,y) and (y,x) then x=y.

    This is the anti-symettrical property. Check it and convice your self it is true.

    Ah! But your problem is that there are no anti-symettrical pairs, for example given (2,1) there is no (1,2). So what! Is it false? No!

    This is a strange situation when a statement is true, note, it is never violated.

    In symbolic logic,

    (x,y) \wedge (y,x) \to x=y

    This is a conditional statement. Meaning If .... then .... When is a conditional false? When a true statement implies a false statement. Since the initial statement (hypothesis) is always false it means it is always a false implying some statement. That statement is therefore true.
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