Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. Some coaches are not drivers.
2. All guards are drivers.
Conclusions:
I. Some guards are not coaches.
II. Some coaches are not guards.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only conclusion II follows
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. “Some X are not Y” cannot be read the other way round.
“Some coaches are not drivers”: part of the coaches lies outside the drivers
“All guards are drivers”: the circle of guards lies inside the circle of drivers; nothing is said about guards and coaches
Conclusion I: Some guards are not coaches. — Does not follow. The guards may all be coaches, as in the diagram.
Conclusion II: Some coaches are not guards. — Follows. The coaches who are not drivers cannot be guards, because every guard is a driver.
Conclusion II follows on its own, so “either I or II” does not apply.