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 rafts are boats.
2. All canoes are boats.
3. Some canoes are rentals.
Conclusions:
I. Some rafts are rentals.
II. Some boats are rentals.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 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.
“All rafts are boats”: the circle of rafts lies inside the circle of boats
“All canoes are boats”: the circle of canoes also lies inside the circle of boats; rafts and canoes need not meet
“Some canoes are rentals”: the circles of canoes and rentals overlap
Conclusion I: Some rafts are rentals. — Does not follow. The rentals are linked only with the canoes, and the rafts may be other boats; in the diagram rafts and rentals do not meet.
Conclusion II: Some boats are rentals. — Follows. The canoes that are rentals are boats too, because every canoe is a boat.