**Given:**

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

- 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"

**Statement:**

$$Q \% K @ J & L $ R @ P$$

**Conclusions:**

I. Some K being not R is a possibility

II. All J can be R

III. All Q being L is a possibility

IV. All K can never be R

Which of the conclusions logically follow from the given statements?

Question

**Given:**

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

- 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"

**Statement:**

$$Q \% K @ J & L $ R @ P$$

**Conclusions:**

I. Some K being not R is a possibility

II. All J can be R

III. All Q being L is a possibility

IV. All K can never be R

Which of the conclusions logically follow from the given statements?

Accepted Answer

**Solution:**

Let's analyze the given statement step-by-step using the symbol meanings:

1. $$Q \% K$$ means "Some Q is K."

2. $$K @ J$$ means "All K are J."

3. $$J & L$$ means "Only a few J are L."

4. $$L $ R$$ means "No L is R."

5. $$R @ P$$ means "All R are P."

Now, let's evaluate each conclusion:

- **Conclusion I: Some K being not R is a possibility.**
  - Since $$L$R$$ means no L is R, and only a few J are L, it is possible that some K (which are all J) are not R. However, this is not definitively concluded from the statements, so this is uncertain.

- **Conclusion II: All J can be R.**
  - Since only a few J are L and no L is R, it is possible some J are not L and could be R. But the statement does not guarantee all J can be R.

- **Conclusion III: All Q being L is a possibility.**
  - Since some Q is K, and all K are J, and only a few J are L, it is possible that all Q are L (if Q overlaps with the few J that are L). So this is a possibility.

- **Conclusion IV: All K can never be R.**
  - Since all K are J and only a few J are L, and no L is R, but some J could be R, it is not necessary that all K can never be R. So this conclusion does not follow.

**Hence, only conclusion III logically follows.**

**Answer:** Only III

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