First, I should note that the % you have here is known as the $XOR$ (for which we sometimes use the symbol $\oplus$)
Use induction to show that any expression built up from $P$'s, $Q$'s, and any number of $XOR$'s will have an even number of $1$'s when evaluated on a truth table.
Use induction to show that any expression $\phi$ using any variables and any number of $XOR$'s cannot capture the truth-function that would return True if all variables in $\phi$ are set to False.
Basic Set-up for latter:
Base: $\phi$ is some atomic statement $P$. Clearly this does not capture any truth-function that returns True if $P$ is False.
Step: Suppose $\phi=\phi_1 \ XOR \ \phi_2$, where by inductive hypothesis neither $\phi_1$ nor $\phi_2$ captures any truth-function that returns True when all variables in $\phi_1$ and $\phi_2$ are set to False respectively. Then neither $\phi_1$ nor $\phi_2$ captures any truth-function that returns True when all variables in $\phi$ are set to False, for setting all variables in $\phi$ to False implies setting all variables in $\phi_1$ and in $\phi_2$ to False. This means that when all variables in $\phi$ are set to False, both $\phi_1$ and $\phi_2$ evaluate to False, and hence $\phi = \phi_1 \ XOR \ \phi_2 = False \ XOR \ False = False$ ... meaning that $\phi$ cannot capture any truth-function that returns True when all variables in $\phi$ are set to False.
OK, so that concludes the inductive proof. Are we there yet? Not quite! Because all we have proven is that certain truth-functions as defined over certain variables cannot be proven using an expression built up from $XOR$'s and those very variables, but that does not immediately imply that you couldn't capture that truth-function using an expression built up from $XOR$'s and any variables (i.e including variables that may not be involved with the desired truth-function). To see why this is important, consider what would happen if we could somehow create some expression $\psi$ using some other variables, and suppose that this statement would be equivalent to a tautology ... then $\psi \ XOR \ P$ would be equivalent to $\neg P$, and so we'd be able to express $\neg P$ after all; something we seemed to have ruled out, but now realize might be possible after all.
So, how do we rule out the potential effect of any other variables? Well ... I must say I'm a bit stuck there myself ... Hmmm ... maybe you should go with my original HINT?