Peter states the following facts about the football premiership:

If St Kilda beat Hawthorn, Franklin is included next week

Hawthorn beating St Kilda means that Geelong will top the ladder

Hawthorn will make the top eight only if Carlton miss out on the finals

If Geelong lose to Essendon then Geelong can't top the ladder

If Hawthorn fail to make the top eight, Franklin will be dropped next week

a) Formulate these five facts as statements in propositional logic.

I did this:

p: St Kilda beat Hawthorn

q: Franklin included next week

x: Geelong top the ladder

y: Hawthorn will make the top 8

z: Carlton miss out on finals

a: Geelong lose to Essendon

1.

2.

3.

4.

5.

b) Is it the case that if Geelong don't manage to top the ladder, Carlton miss out

on the finals? Give your reasoning.

So is this part asking whether is true or false?

Do I use rules of inference from my 5 propositions from part a) to figure out b)? I can't seem to link them together...

Any help would be much appreciated!