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 doctors are advisers.
2. All teachers are advisers.
3. Some chefs are advisers.
4. All chefs are businessmen.
Conclusions:
I. Some teachers are doctors.
II. Some businessmen are advisers.
III. Some businessmen are teachers.
IV. Some advisers are teachers.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only conclusions II and IV 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.
“Some doctors are advisers”: the circles of doctors and advisers overlap
“All teachers are advisers”: the circle of teachers lies inside the circle of advisers; it need not meet the doctors
“Some chefs are advisers”: the circles of chefs and advisers overlap
“All chefs are businessmen”: the circle of chefs lies inside the circle of businessmen
Conclusion I: Some teachers are doctors. — Does not follow. Both meet the advisers, but the doctors may meet advisers who are not teachers, as in the diagram.
Conclusion II: Some businessmen are advisers. — Follows. The chefs who are advisers are also businessmen, because all chefs are businessmen.
Conclusion III: Some businessmen are teachers. — Does not follow. The statements join the businessmen to the advisers only through the chefs, and the teachers may be other advisers; in the diagram the two do not meet.
Conclusion IV: Some advisers are teachers. — Follows. Every teacher is an adviser, so the teachers themselves are advisers who are teachers.