In the following questions , there are statements followed by conclusions . Choose the conclusions which must logically follow from the given statements .
Statements :
1. Some students are orators .
2. All orators are goalkeepers .
3. Some goalkeepers are honest
Conclusions :
I. Some students are honest
II. Some goalkeepers are students

Options

A. Only conclusion I
B. Only conclusion II
C. Both conclusion I and II
D. Neither conclusion I nor II

Answer

To solve the problem, we will analyze the statements and conclusions using a step-by-step approach.

### Step 1: Analyze the Statements
1. **Statement 1**: Some students are orators.
- This indicates that there is an overlap between the set of students and the set of orators.

2. **Statement 2**: All orators are goalkeepers.
- This means that the set of orators is completely contained within the set of goalkeepers.

3. **Statement 3**: Some goalkeepers are honest.
- This indicates that there is an overlap between the set of goalkeepers and the set of honest individuals.

### Step 2: Draw the Venn Diagram
- Draw three circles:
- Circle A for Students
- Circle B for Orators (which is completely inside Circle C for Goalkeepers)
- Circle C for Goalkeepers
- Circle D for Honest individuals (which overlaps with Circle C)

### Step 3: Analyze the Conclusions
1. **Conclusion I**: Some students are honest.
- From the Venn Diagram, we cannot definitively conclude that some students are honest. The overlap between students and honest individuals is not guaranteed based on the given statements. Therefore, this conclusion does not logically follow.

2. **Conclusion II**: Some goalkeepers are students.
- Since some students are orators and all orators are goalkeepers, it follows that those students who are orators are also goalkeepers. Thus, there is a logical conclusion that some goalkeepers are indeed students.

### Step 4: Final Conclusion
- Based on the analysis:
- **Conclusion I** is not valid.
- **Conclusion II** is valid.

Thus, the answer is that **only Conclusion II follows** from the given statements.

### Final Answer
Only Conclusion II follows from the statements.

---