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 gardeners are cyclists.
2. All gardeners are painters.
Conclusions:
I. Some cyclists are painters.
II. Some painters are cyclists.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both conclusions I and II follow
A conclusion follows only if it is true in every diagram that fits the statements; each class named in a statement is taken to have members. A “some” statement can be read the other way round: “some X are Y” means the same as “some Y are X”.
“All gardeners are cyclists”: the circle of gardeners lies inside the circle of cyclists
“All gardeners are painters”: the circle of gardeners also lies inside the circle of painters
Conclusion I: Some cyclists are painters. — Follows. The gardeners are cyclists and also painters, so at least the gardeners are cyclists who are painters.
Conclusion II: Some painters are cyclists. — Follows. It is conclusion I read the other way round, so it is true whenever conclusion I is.