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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.

If $\text{G}$ is not sent to negotiate, then which of the following is a complete and accurate list of pilots who must be sent to negotiate?

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

Option B. A, B, H, F

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

We cannot add E, if we add E then we need to remove the H and for removal of H we need to remove A and so on.

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8 Comments

Why CD must be there?
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C and D strongly complement each other.[condition 6]
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Condition 6 says “CD” must be present together or absent together.
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that is what I meant by word strongly complement each other.

Here I am taking complement as Aggregate, Company.
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Well the point is “C” and “D” need not go and all the given conditions are satisfied.
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But it question they have asked about “complete and accurate list”. Without adding C and D the list will be incomplete.
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complete and accurate list of pilots who must be sent

Question is asking for the list of people who "must be" sent. CD need not be sent. Instead of "must be" if the question was "can be", then CD will be there. That is, presence of CD is optional.

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Thanks, I got it now.
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Answer:

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