Question : Direction: In the following question, two statements are given followed by four conclusions I, II, III, and IV. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements.

Statements

Some cars are buses.

All cars are caves.

Conclusions

I. Some caves are not buses.

II. Some caves are buses.

III. No cave is a bus.

IV. Some caves are cars.

Option 1: Only conclusion I follows

Option 2: Only conclusion II follows

Option 3: Only conclusion II and IV follow

Option 4: Only conclusion IV follows

Correct Answer: Only conclusion II and IV follow

Solution : Let's evaluate the conclusions based on the given statements:

Statements

1. Some cars are buses.
2. All cars are caves.

Venn diagram

Now, let's consider each conclusion:

I. Some caves are not buses.

• This conclusion is not true based on the given statements. Since some cars are buses (Statement 1) and all cars are caves (Statement 2), it does not logically follow that some caves are not buses. Some caves are only for cars and nothing can be said about being buses or not.

II. Some caves are buses.

• This conclusion is also true based on the given statements. Statement 1 states that some cars are buses, and since all cars are caves (Statement 2), it follows that some caves are indeed buses.

III. No cave is a bus.

• This conclusion is not true based on the given statements. Statement 1 explicitly states that some cars are buses, which means there is at least one cave (cars) that is also a bus.

IV. Some caves are cars.

• This conclusion is true based on the given statements. Since all cars are caves (Statement 2) and some cars are buses (Statement 1), it logically follows that some caves are cars.

In summary, conclusions II and IV are true based on the given statements, while conclusions I and III are not true.

Hence, the third option is correct.