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Eight fighter pilots flying over a conflict region notice some hostile activity taking place in a village. To peaceably resolve the conflict, they land their planes and decide that it would be best to send those pilots who would best complement each other as negotiators to talk to the warring parties. The pilots $\text{A, B, C, D, E, F, G,}$ and $\text{H}$ are chosen as negotiators according to the following conditions:

  1. $\text{A}$ is chosen if $\text{B}$ is chosen.
  2. If $\text{G}$ is not chosen, then $\text{A}$ and $\text{F}$ are chosen.
  3. $\text{B}$ and $\text{H}$ are chosen if $\text{A}$ is chosen
  4. If $\text{F}$ is not chosen, then $\text{G}$ is chosen
  5. If $\text{H}$ is not chosen, then $\text{E}$ is chosen.
  6. If $\text{C}$ is not chosen, then $\text{D}$ is not chosen, and if $\text{D}$ is not chosen , then $\text{C}$ is not chosen.

Which of the following could be a complete group of negotiators?

  1. $\text{F, A, H, B}$
  2. $\text{G, D, C}$
  3. $\text{E, A, H, F}$
  4. $\text{A, B, F, G}$
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Option A. F, A, H, B

We can re-write the conditions as 

$B \rightarrow A$

$G_{not} \rightarrow A, F$

$A \rightarrow B, H$

$F_{not} \rightarrow G$

$H_{not} \rightarrow E$

$C_{not} \rightarrow D_{not} $ & $D_{not} \rightarrow C_{not}$

Option C – wrong  $\because$ E and H can not be in same group

Option D – wrong  $\because$ F and G can not be in the same group


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Correct Answer: (A)



This game introduces the idea of reciprocal causation. For example, the constraint that says “If $A$, then $B$, and if $B$, then $A$” should be transcribed in one of the following two ways, based on the configurations of the other variables in the diagram:

You will run into reciprocal causation in the final constraint of this logic game. Here are the final diagrams that you should create:

Notice how the reciprocal causation constraints are diagrammed. Be aware of the implications of these constraints. For instance, if $B$ is not sent (diagram B), then $A$ cannot be sent and $G$ must be sent. In diagram A, if $B$ is sent, then $A$ and $H$ are sent.

Which of the following could be a complete group of the negotiators?

(A) $F, A, H,$ and $B$ could all be sent.

(B) If $H$ is not sent, then $E$ must be sent.

(C) If $A$ is sent, then $B$ must be sent.

(D) If $A$ is sent, then $H$ must be sent.

(A) is the correct answer.


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