Analyze Team Selection Rules

The objective is to find a valid team of 5 members chosen from individuals A, B, C, D, E, F, P, Q, R, and T, following a set of specific constraints.

Selection Constraints

• Team Size: The team must consist of exactly 5 members.
• Condition 1 (A, E, F): Members A, E, and F must be selected together. They form a single unit.
• Condition 2 (B, Q, D): If member B is selected, then members Q and D cannot be part of the team.
• Condition 3 (C, E, F): Member C cannot be selected simultaneously with either E or F.
• Condition 4 (B, T): From the pair {B, T}, only one member can be selected at most.

Evaluate Each Option

Each provided option is checked against the five selection constraints.

Option 1: {A, B, E, P, R}

• Analysis: This selection includes A and E but excludes F.
• Rule Violation: Fails Condition 1, as A, E, and F must be selected together.

Option 2: {D, P, R, C, Q}

• Analysis: This team has 5 members: D, P, R, C, and Q.
• Constraint Check:
  • Condition 1 (A, E, F): None of A, E, or F are selected. Satisfied.
  • Condition 2 (B, Q, D): B is not selected, so the constraint (If B then no Q, D) is met. Q and D are selected, which is permissible as B is absent. Satisfied.
  • Condition 3 (C, E, F): C is selected, but E and F are not. Satisfied.
  • Condition 4 (B, T): Neither B nor T is selected. This means at most one is selected from the pair {B, T}. Satisfied.
• Result: This option fulfills all the specified conditions.

Option 3: {B, P, R, C, T}

• Analysis: This team includes both B and T.
• Rule Violation: Fails Condition 4, which allows at most one member from the pair {B, T} to be selected.

Option 4: {A, B, C, E, F}

• Analysis: This team includes C along with E and F.
• Rule Violation: Fails Condition 3, as C cannot be selected with E or F.

Option 5: Incomplete Option

• Analysis: This option does not list 5 members.
• Rule Violation: Fails the basic requirement of selecting exactly 5 members.

Conclusion on Correct Selection

After evaluating all options against the given rules, Option 2 ({D, P, R, C, Q}) is the only selection that satisfies all the constraints for forming the group captain's team.