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The question is based on the information provided below.

A number of dacoits need to hole up in their hideout. The problem is that, as with many criminal groups, there are a number of personality conflicts that disallow certain members of the dacoit group from being in the hideout at the same time as certain other members. The personality issues of the bandits $\text{A, B, C, D, E, F, G,}$ and $\text{H}$ are illuminated by the following constraints:

  1. If $\text{D}$ is in the hideout, then $\text{E}$ is in the hideout.
  2. If $\text{E}$ is not in the hideout, then $\text{A}$ is in the hideout.
  3. If $\text{B}$ is not in the hideout, then $\text{C}$ is not in the hideout.
  4. If $\text{F}$ is in the hideout, then $\text{H}$ is not in the hideout.
  5. If $\text{A}$ is not in the hideout, then $\text{B}$ is in the hideout.

If $\text{F}$ must be in the hideout when $\text{A}$ or $\text{B}$ is in the hideout, then which of the following must be true?

  1. $\text{C}$ is never outside of the hideout
  2. $\text{C}$ and $\text{B}$ are always in the hideout
  3. $\text{H}$ is never in the hideout
  4. $\text{D}$ and $\text{E}$ are always in the hideout
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Correct Answer: (C)

Explanation:

 

If $F$ must be in the hideout when $A$ or $B$ is in the hideout, then which of the following must be true?

(C) This question adds a constraint to the game, and you should add marks to your diagrams to represent this additional constraint. It is generally not wise to add marks directly to your diagram from individual questions, since these question-constraints will not influence the game aside from that one question. Many people still mark the question-constraint in pencil and then erase it after the question is over. Here is what your diagram would look like:

You see in both scenarios that $F$ must be in the hideout and $H$ must be out of the hideout.

(A) Negation possible in diagram B.

(B) Negation possible in diagram B.

(D) Negation possible in diagram B.

(E) C is the correct answer.

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