Given the symbolic meanings:

- $A@B$ 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"

Consider the statement:

$$F \% J \$ G \& C @ E$$

Evaluate the following conclusions:

I. All C can never be F

II. Some G is not E

III. All F being G is not a possibility

IV. Some J being E is a possibility

Which of the following conclusions logically follow from the given statement?

Question

Given the symbolic meanings:

- $A@B$ 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"

Consider the statement:

$$F \% J \$ G \& C @ E$$

Evaluate the following conclusions:

I. All C can never be F

II. Some G is not E

III. All F being G is not a possibility

IV. Some J being E is a possibility

Which of the following conclusions logically follow from the given statement?

Accepted Answer

**Solution:**

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

2. Analyze each conclusion:

- **Conclusion I: All C can never be F**
     Since some F is J and no J is G, and only a few G are C, and all C are E, there is no direct information to say all C can never be F. So, this conclusion does not necessarily follow.

- **Conclusion II: Some G is not E**
     Given all C are E and only a few G are C, it implies some G may not be C and hence may not be E. So, this conclusion could be true.

- **Conclusion III: All F being G is not a possibility**
     Since some F is J and no J is G, it is impossible for all F to be G. So, this conclusion follows.

- **Conclusion IV: Some J being E is a possibility**
     Since all C are E and only a few G are C, and no J is G, it is possible that some J could be E (not contradicted). So, this conclusion follows.

3. From the above, conclusions III and IV logically follow.

**Answer:** Both III and IV

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