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 surveyors are engineers.
2. Some engineers are not managers.
Conclusions:
I. Some surveyors are not managers.
II. Some managers are not surveyors.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither conclusion I nor 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.
“All surveyors are engineers”: the circle of surveyors lies inside the circle of engineers
“Some engineers are not managers”: part of the engineers lies outside the managers; these may be engineers who are not surveyors, so nothing is fixed about surveyors and managers
Conclusion I: Some surveyors are not managers. — Does not follow. In the first diagram all surveyors are managers; the engineers outside the managers are other engineers.
Conclusion II: Some managers are not surveyors. — Does not follow. In the second diagram all managers are surveyors.
I and II are not an either-or pair: when surveyors and managers only partly overlap, both are true at once; and in a diagram with the same members in the two circles, both are false.