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Math Help - property of function

  1. #1
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    property of function

    Hi, i was wondering if someone can help me understand about this problem.

    Prove that a function F: R x R --> R satisfy any two of the properties
    a)VxVy[F(x,y)=F(y,x)]
    b)VxVy[F(x,y)=F(-x,-y)
    c)VxVy[(F(x,y)=F(-y,-x)]
    must also satisfy the third.

    (VxVy stands for all x and for all y)




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  2. #2
    MHF Contributor

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    I will do one of the three. You must do the other two!
    Suppose that {\color{blue}F(x,y) = F(y,x)}\, \wedge \,{\color{red}F(x,y) = F( - x, - y)}.
    Then {\color{blue}F(a,b) = F(b,a)} = {\color{red}F(b,a) = F( - b, - a)}
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