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The question is based on the information provided below:

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.

What is the greatest number of pilots that could be sent to negotiate?

1. $5$
2. $6$
3. $7$
4. $8$

### 1 comment

option:--> B=6:

Option B. 6

We can re-write the conditions as

$B \rightarrow A$

$G_{not} \rightarrow A, F$

$A \rightarrow B, H$

$F_{not} \rightarrow G$

$H_{not} \rightarrow E$

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

So greatest number of pilots that could be sent to negotiate is 6 [A, B, C, D, F and H]

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Explanation:

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.

What is the greatest number of pilots that could be sent to negotiate?

(D) It is possible, using diagrams A and C, to see that all eight plots could be sent to negotiate.

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878 points