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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.

If $\text{H}$ is not sent to negotiate, then which of the following must NOT be true?

  1. $\text{F}$ is sent to negotiate
  2. $\text{E}$ is sent to negotiate
  3. $\text{B}$ is sent to negotiate
  4. $\text{G}$ is sent to negotiate
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Option C. B is sent to negotiate

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

 

If H is not sent to negotiate then A can not be sent to negotiate, and if A can not be sent to negotiate then B also can not be sent to negotiate [from condition 1 and 3]

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