Some tables are shelves. Some shelves are chairs. All chairs are bench...
Given Information:
- Some tables are shelves.
- Some shelves are chairs.
- All chairs are benches.
Conclusions:
i. At least one bench is a table
ii. At least one shelf is a bench
iii. At least one chair is a table
iv. All benches are chairs.
Explanation:
To deduce the conclusions, let's analyze the given information and each conclusion one by one.
i. At least one bench is a table:
- From the given information, we know that some tables are shelves.
- However, there is no direct information about the relationship between tables and benches.
- Therefore, we cannot deduce that at least one bench is a table.
- This conclusion is not valid.
ii. At least one shelf is a bench:
- From the given information, we know that some shelves are chairs.
- However, there is no direct information about the relationship between shelves and benches.
- Therefore, we cannot deduce that at least one shelf is a bench.
- This conclusion is not valid.
iii. At least one chair is a table:
- From the given information, we know that some tables are shelves.
- We also know that some shelves are chairs.
- Therefore, there is a possibility that some chairs can be tables indirectly through the relationship: chairs -> shelves -> tables.
- This conclusion is valid.
iv. All benches are chairs:
- From the given information, we know that all chairs are benches.
- Therefore, it can be deduced that all benches are chairs.
- This conclusion is valid.
Conclusion:
Based on the analysis, the valid conclusions are:
- At least one chair is a table (iii)
- All benches are chairs (iv)
Hence, the correct answer is option 'B': Only ii.