If Palermo is at Randsborough, then which one of the following must be true?

Skylar June 16, 2020

@EugeneC, happy to help!

In this specific game, I suggest looking at the rules individually rather than trying to combine them, especially with compound statements. The game still works, and you may notice that none of our scenarios throughout the game place L in S, thereby avoiding the issue altogether.

Each doctor (JKLNOP) is in exactly one of the two clinics.
1: J(s) -> K(r)
K(s) -> J(r)
2: J(r) -> O(s)
O(r) -> J(s)
3: L(s) -> N(r) and P(r)
N(s) or P(s) -> L(r)
4: N(r) -> O(r)
O(s) -> N(s)
5: P(r) -> K(s) and O(s)
K(r) or O(r) -> P(s)

This question tells us that P is at R.
r: P
s:

Our first step should be to look through our individual rules for statements where P(r) is the sufficient condition. Rule #5 says that if we have P(r), we must also have K(s) and O(s).
r: P
s: KO

Now we should look for statements where either K(s) or O(s) are sufficient. The contrapositive of Rule #1 says that if we have K(s), we must also have J(r). The contrapositive of Rule #4 says that if we have O(s), we must also have N(s).
r: PJ
s: KON

Lastly, we should look for statements where either J(r) or N(s) are sufficient. Rule #2 says that if we have J(r), we must also have O(s). We already have this placed. The contrapositive of Rule #3 says if we have N(s), we must also have L(r).
r: PJL
s: KON

This is our final diagram for the question, which makes (A) correct.

Does that make sense? Hope it helps! Please let us know if you have any other questions!

Connie-Ticho July 15, 2020

When I looked at the conditions and noticed that this didn't seem to make sense, I listed L as going into R on my diagram because
I knew that it couldn't go into S without the game not making sense. Would this have been okay?

heyitsnattt March 24, 2021

Why did you reverse all the rules rather than reverse and negate ?