Problem Analysis

The task is to select a team of 6 players from 9 available players (A, B, C, D, E, F, G, H, M), adhering to several specific constraints.

Team Selection Constraints

• Constraint 1: Player A and Player B cannot be selected together.
• Constraint 2: Player G and Player H cannot be selected together.
• Constraint 3: Player H and Player A must be in the team together (either both in or both out).
• Constraint 4: Player E and Player F cannot be selected together.
• Constraint 5: Player C and Player H cannot be selected together.
• Constraint 6: Player C and Player D must always be selected together.

Evaluating Team Options

Let's examine each option based on the constraints:

1. Option 1: {A, D, G, E, C, H}
   • Violates Constraint 2 (G and H selected together).
   • Violates Constraint 5 (C and H selected together).
2. Option 2: {B, C, D, E, H, M}
   • Violates Constraint 3 (H is selected, but A is not).
   • Violates Constraint 5 (C and H selected together).
3. Option 3: {A, C, D, E, G, M}
   • Violates Constraint 3 (A is selected, but H is not).
4. Option 4: {B, C, D, E, G, M}
   • Team size is 6. (Ok)
   • Constraint 1 (A, B): B is selected, A is not. (Ok)
   • Constraint 2 (G, H): G is selected, H is not. (Ok)
   • Constraint 3 (H, A): Neither H nor A is selected. (Ok)
   • Constraint 4 (E, F): E is selected, F is not. (Ok)
   • Constraint 5 (C, H): C is selected, H is not. (Ok)
   • Constraint 6 (C, D): C and D are both selected. (Ok)
   • This option satisfies all constraints. (Ok)

Conclusion

The selection {B, C, D, E, G, M} is the only option that meets all the specified requirements for team formation.