I am trying to convert the following into propositional logic in order to construct a semantic tableaux:
If Mark goes to the party, then so does Pat. John or Pat will go to the party. John will not go to the party unless Steve goes to the party. Steve does not go the party and neither does Mark. Therefore, Pat does go to the party.
What I have gotten so far is $M \implies P$, $J \lor P$,$\neg S \land \neg M$,$\neg P$
I am not sure how to translate "John will not go to the party unless Steve goes to the party."
Thanks in advance for any help given!
A statement '$P $ unless $Q$' typically translates to '$P$ if not $Q$', i.e. $\neg Q \rightarrow P$
Here is an example:
'You fail ($F$) the course unless you complete ($C$) all the HW's'
OK, so if someone does not complete all the HW's they will clearly fail the course: $\neg C \rightarrow F$
Ok, but will you pass the course if you do complete all the HW's? No, not necessarily .. you may also have to do well on the final, for example. So, we cannot say $C \rightarrow \neg F$ ... so it is not a biconditional.