Which of the following selection is correct?
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.
Similar Questions
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