Step-by-Step Team Selection

To find the maximum size of a team that includes G, we will start with G on the team and apply all the given rules to see who else must be included or excluded. Our goal is to add as many players as possible without violating any conditions.

1. Initial Deductions from Including G

We start with the team having player G: Team = {G, ...}

• Rule 5 states: "The team must include exactly one among C, G and I."
  Since G is on the team, it logically follows that C and I must be excluded.
• Rule 4 states: "If the includes G, it must also include F."
  Since G is on the team, F must also be on the team.

At this point, we have:
Team Members (IN): {G, F}
Excluded Members (OUT): {C, I}

2. Maximizing the Team Size

Now, we will make choices for the remaining players (A, B, D, E, H, J) with the goal of maximizing the team's size.

• Rule 3 (E or B): "The team must include E or B, but not both."
  To maximize the team, we must add one of them. Let's choose to add E. This means B must be excluded.
  Current Team: {G, F, E, ...}
• Rule 8 (A and D): "The team must include both A and D or neither of them."
  To maximize the team, we should try to add both A and D.
  Current Team: {G, F, E, A, D, ...}
• Consequence of adding D (Rule 7): "D and H cannot be members of the same team."
  Since we have added D, it follows that H must be excluded.
• Checking the last player, J: Can J be on the team?
  Rule 2 states: "If the team includes J, it must also include F." Our team already includes F, so this condition is satisfied. We can add J to the team.

3. Final Team Composition and Verification

By making choices that maximize the size, we have arrived at the following team:

Final Team = {G, F, E, A, D, J}

Let's verify this team against all rules:

• Size: 6 members.
• Minimum Roles: The team has Forwards (A, E, J), Point Guards (G), and Defenders (F, D). All minimums are met.
• All 8 rules are satisfied by this composition.

Conclusion

The maximum possible size of the team that includes G is 6.