Hmmm, it seems I am stuck with a further extension of this problem.

The extension is that "can one deduce that either Geelong lose to Essendon or Carlton make the finals?"

So my interpretation of this question is that is $\displaystyle a \lor \neg z$ true or false?

Now to prove this, if $\displaystyle a$ is true or $\displaystyle \neg z$ is true then $\displaystyle a \lor \neg z$ is true, however if $\displaystyle a$ and $\displaystyle \neg z$ are both false, then $\displaystyle a \lor \neg z$ is false.

But no matter how hard I try, I can not seem to find any way of manipulating the information we have to prove what I described above