Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. All buckets are containers.
2. All baskets are containers.
Conclusions:
I. Some buckets are baskets.
II. No bucket is a basket.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Either conclusion I or conclusion II follows
When two conclusions do not follow on their own, but in every diagram exactly one of them is true (such as “some X are Y” and “no X is Y”), the answer is “either one or the other follows”.
“All buckets are containers”: the circle of buckets lies inside the circle of containers
“All baskets are containers”: the circle of baskets also lies inside the circle of containers; buckets and baskets may meet or may not
Conclusion I: Some buckets are baskets. — Does not follow on its own. In case 2 the buckets and baskets do not meet, so it is false there.
Conclusion II: No bucket is a basket. — Does not follow on its own. In case 1 some buckets are baskets, so it is false there.
Buckets and baskets either meet or they do not; there is no third case. So in every diagram exactly one of I and II is true: either conclusion I or conclusion II follows.