Game Setup
This is a very weird game. Pay careful attention to the explanations and how I build the diagram, as well as how to read the diagram. Make sure to reread if you don’t fully understand.
It looks like a type of conditional reasoning diagram, from an in-out game.
The complicating factor in this game is that people just aren’t in or out. There are three groups: Hired, Interviewed, Out.
The first two rules are simple. They tell us that if G is interviewed then J is interviewed. If J is interviewed then L is interviewed.
The next rule is also simple. F is always interviewed.
The fourth rule is worded strangely. Fu is not hired unless Kowalski is interviewed. It means that if you hire Fu then you need to interview Kowalski. Also, you know that if you hire Fu you have to interview Fu. This is always true but we can write it down regardless.
This is the start of a chain. It’s a bit different, but it’s very useful.
The next rule says that if you hire Kowalski then you have to interview Mayer. You also interview Kowalski if you hire Kowalski.
So Kowalski being interviewed is a necessary condition for Kowalski being hired and for Fu being hired.
The way to read this backwards (i.e. contrapositive) is that if you don’t interview Kowalski then you can’t hire Fu or Kowalski.
Lastly, if Mayer is hired and Lee is interviewed then you have to hire Ordoveza. We can add our diagram of G, J and L onto this main diagram.
The diagram is pretty big. It contains all the variables. So, for example, if you interviewed G and you also interview J and L. If you hire M as well, then you must hire O. And since you hire O you must interview O.
Likewise, if you don’t interview O then you can’t hire O. So you must either not have hired M or interviewed L. That’s how we read this diagram.
Here’s the contrapositive:
I didn’t find the contrapositive very useful. Instead I just figured out contrapositives section by section as needed.
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