A team of five members is to be selected among eight members A, B, C, D, E, F, G and H. C and F have to be selected together. Either G or D has to be selected with A. B or E has to be selected with H. G and C cannot be selected together. Which of the following members can be selected?
Team Selection Problem: Finding a Valid 5-Member Team
This problem asks us to find a valid team of five members from a group of eight (A, B, C, D, E, F, G, H), based on specific rules or constraints regarding which members can or must be selected together.
Understanding the Members and Constraints
We have 8 potential members: A, B, C, D, E, F, G, H.
The rules for selecting a team of 5 are:
- Condition 1: C and F must be selected together. This means if C is in the team, F must be in the team, and if F is in the team, C must be in the team. If neither is selected, the condition is met.
- Condition 2: Either G or D has to be selected with A. This means if member A is selected, then exactly one of G or D must also be selected with A. A cannot be selected without G or D, or with both G and D.
- Condition 3: B or E has to be selected with H. This means if member H is selected, then at least one of B or E must also be selected with H. H cannot be selected without at least one of B or E.
- Condition 4: G and C cannot be selected together. If G is in the team, C cannot be, and vice-versa.
Step-by-Step Analysis of Team Options
We will examine each given option to see if it satisfies all four conditions for a 5-member team.
Option 1: ABCDE Analysis
Team members: {A, B, C, D, E}
- Team Size: 5 members. Correct.
- Condition 1 (C and F together): Member C is selected, but member F is not selected. This violates Condition 1.
Since Condition 1 is violated, this team is not valid. We don't need to check the other conditions, but for completeness:
- Condition 2 (A with G or D): Member A is selected, and member D is selected. This satisfies the rule that if A is selected, either G or D must be with A (here, D is with A). This part is OK.
- Condition 3 (H with B or E): Member H is not selected. This condition does not apply. This part is OK.
- Condition 4 (G and C not together): Member G is not selected, and member C is selected. They are not together. This part is OK.
Conclusion for Option 1: Invalid due to violation of Condition 1.
Option 2: ABCFG Analysis
Team members: {A, B, C, F, G}
- Team Size: 5 members. Correct.
- Condition 1 (C and F together): Members C and F are both selected. This satisfies Condition 1. This part is OK.
- Condition 2 (A with G or D): Member A is selected, and member G is selected (D is not). This satisfies the rule that if A is selected, either G or D must be with A (here, G is with A). This part is OK.
- Condition 3 (H with B or E): Member H is not selected. This condition does not apply. This part is OK.
- Condition 4 (G and C not together): Members G and C are both selected. This violates Condition 4.
Conclusion for Option 2: Invalid due to violation of Condition 4.
Option 3: BCDFG Analysis
Team members: {B, C, D, F, G}
- Team Size: 5 members. Correct.
- Condition 1 (C and F together): Members C and F are both selected. This satisfies Condition 1. This part is OK.
- Condition 2 (A with G or D): Member A is not selected. This condition does not apply directly. This part is OK.
- Condition 3 (H with B or E): Member H is not selected. This condition does not apply. This part is OK.
- Condition 4 (G and C not together): Members G and C are both selected. This violates Condition 4.
Conclusion for Option 3: Invalid due to violation of Condition 4.
Option 4: BCDEF Analysis
Team members: {B, C, D, E, F}
- Team Size: 5 members. Correct.
- Condition 1 (C and F together): Members C and F are both selected. This satisfies Condition 1. This part is OK.
- Condition 2 (A with G or D): Member A is not selected. This condition does not apply directly. This part is OK.
- Condition 3 (H with B or E): Member H is not selected. This condition does not apply directly. This part is OK.
- Condition 4 (G and C not together): Member G is not selected, and member C is selected. They are not together. This satisfies Condition 4. This part is OK.
All conditions are satisfied for Option 4.
Conclusion for Option 4: Valid.
Conclusion: Identifying the Valid Team Selection
Based on the analysis of each option against the given rules, only the team comprising members B, C, D, E, and F satisfies all the selection criteria.
Revision Table: Quick Check of Team Selection Conditions
| Option | Team Members | Size 5? | Condition 1 (C<->F)? | Condition 2 (A->G^D)? | Condition 3 (H->B|E)? | Condition 4 (~(G&C))? | Valid? |
|---|---|---|---|---|---|---|---|
| 1 | {A, B, C, D, E} | Yes | No (C but no F) | Yes (A with D) | N/A (No H) | Yes (~G, C ok) | No |
| 2 | {A, B, C, F, G} | Yes | Yes (C and F) | Yes (A with G) | N/A (No H) | No (G and C) | No |
| 3 | {B, C, D, F, G} | Yes | Yes (C and F) | N/A (No A) | N/A (No H) | No (G and C) | No |
| 4 | {B, C, D, E, F} | Yes | Yes (C and F) | N/A (No A) | N/A (No H) | Yes (~G, C ok) | Yes |
Additional Information: Logic and Team Selection
This type of problem is a form of logical reasoning or constraint satisfaction problem. You are given a set of items (members) and rules (conditions) that restrict how these items can be combined. To solve it, you systematically check if a proposed combination (team) follows all the given rules.
Key strategies used here include:
- Listing all members and rules clearly.
- Breaking down each rule into specific requirements (e.g., "C and F have to be together" means both must be present or both absent).
- Checking each potential solution against every rule, one by one.
- Eliminating options as soon as a rule is broken.
- Using a table can help keep track of which rule is satisfied or violated by each option.
Understanding logical connectors like "and", "or", "if...then", and "not" is crucial for correctly interpreting the conditions in such problems. These problems test your ability to apply logical rules systematically to reach a valid outcome.
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