# Math Help - property of function

1. ## 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)

2. 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 ${\color{blue}F(a,b) = F(b,a)} = {\color{red}F(b,a) = F( - b, - a)}$