Analyze Team Selection Constraints

The problem requires selecting a team of 5 members from 6 men and 6 women, subject to specific conditions. We will evaluate each option against these conditions.

Conditions Recap:

• Team Size: 5 members.
• Cond 1: C and U must be selected together.
• Cond 2: If B is selected, neither U nor Q can be selected.
• Cond 3: Exactly two members must be selected from the group {A, B, S, T}.
• Cond 4: If E is selected, neither S nor B can be selected.
• Cond 5: If A is selected, B must be selected.

Evaluate Each Option

We check each option step-by-step:

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

• Cond 1 Violation: C is selected, but U is not. This violates the rule that C and U must be together.

Result: Invalid.

Option 2: {P, R, S, T, D}

• Team size is 5.
• Cond 1 Check: Neither C nor U is selected. This is consistent (they are together by not being selected).
• Cond 5 Check: A is not selected. Consistent.
• Cond 4 Check: E is not selected. Consistent.
• Cond 2 Check: B is not selected. Consistent.
• Cond 3 Check: S and T are selected. Exactly two members from {A, B, S, T}. Consistent.

Result: All conditions are met. This is a valid selection.

Option 3: {P, R, A, B, S}

• Cond 3 Violation: A, B, and S are selected. This means three members (A, B, S) are selected from the group {A, B, S, T}, violating the "exactly two" rule.

Result: Invalid.

Option 4: {C, U, A, B, S}

• Cond 2 Violation: B is selected, but U is also selected. This violates the rule that if B is selected, U cannot be selected.

Result: Invalid.

Option 5: (No members listed)

Result: Incomplete/Invalid.

Conclusion

Only Option 2 satisfies all the given constraints for team selection.