Statements: 1. All apples are oranges
2. Some oranges are papayas
Conclusions: 1. Some apples are papayas
2. Some papayas are apples

Options

A. only conclusion 1 follows,
B. only conclusion 2 follows,
C. either conclusion 1 or 2 follows,
D. neither conclusion 1 nor 2 follows,

Answer

To solve the problem, we will analyze the given statements and conclusions step by step.

### Step 1: Understand the Statements
1. **Statement 1**: All apples are oranges.
- This means that every apple is included in the category of oranges.

2. **Statement 2**: Some oranges are papayas.
- This indicates that there is at least one orange that is also a papaya.

### Step 2: Visualize with Venn Diagrams
- Draw a Venn diagram to represent the relationships:
- Draw a large circle for oranges.
- Inside this circle, draw a smaller circle for apples (since all apples are oranges).
- Draw another circle that overlaps with the orange circle to represent papayas (since some oranges are papayas).

### Step 3: Analyze the Conclusions
1. **Conclusion 1**: Some apples are papayas.
- In the Venn diagram, we see that while all apples are within the orange circle, there is no direct overlap between the apple circle and the papaya circle. Therefore, we cannot conclude that some apples are papayas.
- **Conclusion**: This conclusion is **false**.

2. **Conclusion 2**: Some papayas are apples.
- Similar to the first conclusion, there is no overlap between the apple circle and the papaya circle in the Venn diagram. Hence, we cannot conclude that some papayas are apples.
- **Conclusion**: This conclusion is also **false**.

### Final Conclusion
Both conclusions are false based on the analysis of the statements and the Venn diagram.

### Summary of Solution
- **Conclusion 1**: False
- **Conclusion 2**: False
- Therefore, the answer is that **neither conclusion 1 nor conclusion 2 follows**.