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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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