**Statements:**

- All Train is Bus
- No Truck is Auto
- Only a few Truck are Bus

**Conclusions:**

I. All Bus being Auto is a possibility
II. All Train being Auto is a possibility
III. Some Bus is not Auto

Which of the following conclusions logically follow from the given statements?

Question

**Statements:**

- All Train is Bus
- No Truck is Auto
- Only a few Truck are Bus

**Conclusions:**

I. All Bus being Auto is a possibility
II. All Train being Auto is a possibility
III. Some Bus is not Auto

Which of the following conclusions logically follow from the given statements?

Accepted Answer

**Solution:**

1. From the statements:
   - All Train is Bus means every Train is included in Bus.
   - No Truck is Auto means Truck and Auto are mutually exclusive.
   - Only a few Truck are Bus means some Trucks are Bus, but not all.

2. Analyze Conclusion I: "All Bus being Auto is a possibility"
   - Since No Truck is Auto and some Trucks are Bus, Bus and Auto can overlap partially or fully.
   - So, it is possible that all Bus are Auto.
   - Hence, Conclusion I is possible.

3. Analyze Conclusion II: "All Train being Auto is a possibility"
   - Since all Train are Bus, and Bus can be Auto (from Conclusion I), it is possible that all Train are Auto.
   - Hence, Conclusion II is possible.

4. Analyze Conclusion III: "Some Bus is not Auto"
   - Since some Trucks are Bus and Trucks are not Auto, those Bus which are Trucks cannot be Auto.
   - Therefore, some Bus are definitely not Auto.
   - Hence, Conclusion III follows.

5. Since Conclusion III definitely follows, and Conclusion II is possible, Conclusion I is also possible but not definite.

6. Among the options, only Conclusions II and III logically follow.

**Answer:** Only II and III follow

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