Would it be: For every x.y in W, F(x,y) is in W?
I am not getting the gist of this...
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I find it helpful to write an intermediate step that is halfway between English and symbolic logic.
"Everyone can be fooled by somebody" is the same as "For every person $x$, there exists a person $y$ such that $y$ can fool $x$". If we replace all the English parts with symbols, this becomes "$\forall x \exists y, F(y,x)$". If you like, you could explicitly include the domain and get "$\forall x \in W, \exists y \in W, F(y,x)$", but I think it is clear enough without this.
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"For every $x,y$ in $W$, $F(x,y)$ is in $W$" translates to "For every person $x$ and person $y$ in the world, the statement '$x$ can fool $y$' is a person in the world." Does this statement make sense?
What you're trying to say is that for every person in the world, there is some person in the world who can fool them. That is, for every person $x$ in $W$, there is some person $y$ in $W$ such that $y$ can fool $x$. Symbolically: $$\forall x\in W\:\exists y\in W\:F(y,x)$$
$$\forall x \exists y F(y,x)$$