I have this kind of 'riddle' as a question that i need to complete, however I'm not sure what to do of it.
This is the question:
Determine who out of the following is guilty of doping. The suspects are: Sam, Michael, Bill, Richard, Matt.
1) Sam said: Michael or Bill took drugs, but not both.
2) Michael said: Richard or Sam took drugs, but not both.
3) Bill said: Matt or Michael took drugs, but not both.
4) Richard said: Bill or Matt took drugs, but not both.
5) Matt said: Bill or Richard took drugs, but not both.
^ Of these 5 statements, 4 are true, one is false.
6) Tom said: If Richard took drugs, then Bill took drugs.
^ This statement is guaranteed to be true.
From this information, I deduced:
p : Michael took drugs
q : Bill took drugs
r : Richard took drugs
s : Sam took drugs
t : Matt took drugs
So given this I came up with this:
1) (p ^ ~q) v (~p ^ q)
2) (r ^ ~s) v (~r ^ s)
3) (t ^ ~p) v (~t ^ p)
4) (q ^ ~t) v (~q ^ t)
5) (q ^ ~r) v (~q ^ r)
6) (~r v q)
However, I'm not sure where to go from here. I suppose, I could connect each statement with an
^ as that seems like the next step to do. Then that entire equation would essentially tell me who was guilty? The next step, would obviously be to simplify, and come up with a name. However, I'm not sure how to do this.
Could anyone please shed some light and give me some tips on how to do this?