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 plumbers are golfers.
2. All plumbers are hikers.
Conclusions:
I. Some golfers are hikers.
II. Some hikers are golfers.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 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 plumbers are golfers”: the circle of plumbers lies inside the circle of golfers
“All plumbers are hikers”: the circle of plumbers also lies inside the circle of hikers
Conclusion I: Some golfers are hikers. — Follows. The plumbers are golfers and also hikers, so at least the plumbers are golfers who are hikers.
Conclusion II: Some hikers are golfers. — Follows. It is conclusion I read the other way round, so it is true whenever conclusion I is.