In the following question, symbols &, @, %, and $ represent specific logical relations as follows:

- 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:

$$M \% R @ O & N & P \$\$$$

Analyze the following conclusions:

I. Some O are definitely not N

II. All N being S is not a possibility

III. Some M being O is a possibility

IV. All P can never be R

Which of the following options is correct?

Question

In the following question, symbols &, @, %, and $ represent specific logical relations as follows:

- 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:

$$M \% R @ O & N & P \$\$$$

Analyze the following conclusions:

I. Some O are definitely not N

II. All N being S is not a possibility

III. Some M being O is a possibility

IV. All P can never be R

Which of the following options is correct?

Accepted Answer

**Solution:**

1. Decode the statement step-by-step:
   - $M \% R$ means "Some M is R"
   - $R @ O$ means "All R are O"
   - $O & N$ means "Only a few O are N"
   - $N & P$ means "Only a few N are P"
   - $P \$ \$ means "No P is (something)" — here, double $ signs likely indicate no relation or no A is B for P and the next symbol, but since it's at the end, we consider $P \$\$ as "No P is (some set)" or no further relation.

2. Analyze conclusions:

- **Conclusion I: Some O are definitely not N**
     Since only a few O are N, it means some O are not N. So, conclusion I is true.

- **Conclusion II: All N being S is not a possibility**
     Since N is related to P by "only a few N are P" and no information about S is given, but "All N being S" contradicts the "only a few" relation with P and the fact that N is limited. Hence, conclusion II follows.

- **Conclusion III: Some M being O is a possibility**
     Since some M is R and all R are O, it implies some M can be O. So, conclusion III is possible.

- **Conclusion IV: All P can never be R**
     Since no direct relation between P and R is given, and only a few N are P, and all R are O, it does not conclusively prove that all P can never be R. So, conclusion IV does not follow.

3. Since conclusions I and II definitely follow, the correct option is (a) Both I and II.

**Answer:** Both I and II

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