I dont really see why the answer should be false. The first part of the statement is that 'for all $x$ all $y$..'. Then if $x$ is not equal to $y$, either $P(x,y)$ is true or $P(y,x)$ is true. This seems to be true to me. If $x$ is $1$, the statement is true for $y = 1,~2,~3$ and the same for $x=2,~3$. So where am I going wrong here? Thanks!
You are correct. The formula evaluates to true.