Solve the following exercise by means of a reduction to SAT
- A large company has to form a committee from all of its members to decide its
Each member has a different set of preferences: (i) some do not care about being in the committee,
(ii) others want to be in it either way, (iii) some say that they are okay
not being part of the committee as long as all their chosen representants are in it,
(iv) others say that, if any of the members with whom they have opposite views are part of the committee,
then they must be in it too, and (v) the rest do not want to be part of it under any circumstance.
Moreover, there are pairs of conflictive members, such that not both of them can be in the committee at the same time.
Determine if it is possible to arrange a (non-empty!) committee that satisfies everyone.
The input of the exercise and the output with the solution (when the input is
solvable) are as follows: