A team of four members is to be selected among eight members A, B, C, D, E, F, G and H. C has to be selected with H. B has to be selected with E. F cannot be selected with A. G cannot be selected with H. Which of the following members can be selected?
BEAG
Solving Team Selection with Member Constraints
This question involves selecting a team of four members from a group of eight members (A, B, C, D, E, F, G, H) based on specific conditions or constraints. We need to analyze each given option to determine which one satisfies all the selection rules.
Understanding the Team Selection Rules
Here are the conditions that must be met for a valid team:
- The team must have exactly 4 members.
- Total available members: A, B, C, D, E, F, G, H.
- Constraint 1: C must be selected with H. This means if C is in the team, H must also be in the team, and vice versa. If neither C nor H is in the team, this constraint is satisfied.
- Constraint 2: B must be selected with E. This means if B is in the team, E must also be in the team, and vice versa. If neither B nor E is in the team, this constraint is satisfied.
- Constraint 3: F cannot be selected with A. This means if F is in the team, A cannot be, and if A is in the team, F cannot be. If neither F nor A is in the team, this constraint is satisfied.
- Constraint 4: G cannot be selected with H. This means if G is in the team, H cannot be, and if H is in the team, G cannot be. If neither G nor H is in the team, this constraint is satisfied.
Analyzing Each Option for Validity
Let's examine each provided team option against the given constraints.
Analysis of Option 1: BCEF
- Members: B, C, E, F
- Team size: 4 (Satisfies the size requirement)
- Constraint 1 (C with H): C is present, but H is not. This violates the condition that C must be with H.
Conclusion: Option 1 (BCEF) is not a valid team because it violates Constraint 1.
Analysis of Option 2: ACGH
- Members: A, C, G, H
- Team size: 4 (Satisfies the size requirement)
- Constraint 1 (C with H): Both C and H are present. (Satisfied)
- Constraint 2 (B with E): Neither B nor E is present. (Satisfied)
- Constraint 3 (F cannot be with A): F is not present, A is present. (Satisfied)
- Constraint 4 (G cannot be with H): Both G and H are present. This violates the condition that G cannot be with H.
Conclusion: Option 2 (ACGH) is not a valid team because it violates Constraint 4.
Analysis of Option 3: ABCD
- Members: A, B, C, D
- Team size: 4 (Satisfies the size requirement)
- Constraint 1 (C with H): C is present, but H is not. This violates the condition that C must be with H.
Conclusion: Option 3 (ABCD) is not a valid team because it violates Constraint 1.
Analysis of Option 4: BEAG
- Members: B, E, A, G
- Team size: 4 (Satisfies the size requirement)
- Constraint 1 (C with H): Neither C nor H is present. (Satisfied)
- Constraint 2 (B with E): Both B and E are present. (Satisfied)
- Constraint 3 (F cannot be with A): F is not present, A is present. (Satisfied)
- Constraint 4 (G cannot be with H): G is present, but H is not. (Satisfied)
Conclusion: Option 4 (BEAG) satisfies all the given constraints and is a valid team selection.
Summary of Option Analysis
| Option | Members | Size = 4? | C with H? | B with E? | F not with A? | G not with H? | Valid? |
|---|---|---|---|---|---|---|---|
| 1 | BCEF | Yes | No (C but no H) | No (B & E present) | Yes (no A) | Yes (no H) | No |
| 2 | ACGH | Yes | Yes (C & H present) | Yes (no B & E) | Yes (no F) | No (G & H present) | No |
| 3 | ABCD | Yes | No (C but no H) | No (B & E present) | Yes (no F) | Yes (no H) | No |
| 4 | BEAG | Yes | Yes (no C & H) | Yes (B & E present) | Yes (no F) | Yes (no H) | Yes |
Based on the detailed analysis of each option against all selection constraints, only the team BEAG satisfies all the required conditions.
Revision Table: Key Team Selection Concepts
| Concept | Description | Example (from this problem) |
|---|---|---|
| Mandatory Pair | Two members must be selected together. If one is in the team, the other must also be in the team. If neither is selected, the condition is met. | C must be with H. B must be with E. |
| Forbidden Pair | Two members cannot be selected together in the same team. If one is in the team, the other cannot be. If neither is selected, the condition is met. | F cannot be with A. G cannot be with H. |
| Constraint Checking | Verifying if a proposed solution (team) adheres to all the given rules and conditions. | Checking if BEAG satisfies all four constraints. |
Additional Information: Solving Constraint-Based Problems
Problems like this team selection task are examples of constraint satisfaction problems. These involve finding a solution that fits a set of given rules or limitations.
- Identify Constraints: The first step is always to clearly list all the rules.
- Analyze Options: Systematically check each possible solution (or given options) against every single constraint.
- Eliminate Invalid Options: If an option fails even one constraint, it is not a valid solution.
- Verify Valid Option: Ensure the option identified as valid truly satisfies all constraints simultaneously.
These types of questions test your logical reasoning and ability to follow multiple conditions precisely. Practice with different constraints helps improve problem-solving speed and accuracy.
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