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 dentists are graduates.
2. Some dentists are not singers.
Conclusions:
I. Some graduates are not singers.
II. Some singers are not dentists.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Only conclusion I 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 dentists are graduates”: the circle of dentists lies inside the circle of graduates
“Some dentists are not singers”: part of the dentists lies outside the singers
Conclusion I: Some graduates are not singers. — Follows. The dentists who are not singers are graduates too, because every dentist is a graduate; so these graduates are not singers.
Conclusion II: Some singers are not dentists. — Does not follow. The singers may all be dentists, as in the diagram; “some dentists are not singers” cannot be read the other way round.