In the following question, symbols &, @, %, and $ represent the following relations:

- A@B means "All A are B"
- A&B means "Only a few A are B"
- A$B means "No A is B"
- A%B means "Some A is B"

Given the statement:

$$C$E\%G@B\&D$$

Analyze the following conclusions:

I. All B being D is a possibility

II. Some B being C is not a possibility

III. All G can never be C

IV. All D can be E

Which of the conclusions logically follow from the given statement?

Question

In the following question, symbols &, @, %, and $ represent the following relations:

- A@B means "All A are B"
- A&B means "Only a few A are B"
- A$B means "No A is B"
- A%B means "Some A is B"

Given the statement:

$$C$E\%G@B\&D$$

Analyze the following conclusions:

I. All B being D is a possibility

II. Some B being C is not a possibility

III. All G can never be C

IV. All D can be E

Which of the conclusions logically follow from the given statement?

Accepted Answer

**Solution:**

1. Decode the statement:
   - $C$E$ means No C is E.
   - $E\%G$ means Some E is G.
   - $G@B$ means All G are B.
   - $B\&D$ means Only a few B are D.

2. Analyze each conclusion:

- **Conclusion I: All B being D is a possibility**
     - Since only a few B are D, it means not all B are D. So, "All B being D" is not possible.

- **Conclusion II: Some B being C is not a possibility**
     - Since No C is E and Some E is G, and All G are B, there is no direct relation forbidding some B being C. So, this conclusion does not necessarily follow.

- **Conclusion III: All G can never be C**
     - Since No C is E and Some E is G, it implies C and G cannot overlap. Hence, all G can never be C.

- **Conclusion IV: All D can be E**
     - Since only a few B are D and Some E is G, and All G are B, it is possible that all D can be E.

3. Therefore, conclusions III and IV logically follow.

**Answer:** Both III and IV

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