Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. No belt is a tie.
2. No tie is a cap.
Conclusions:
I. All belts being caps is a possibility.
II. Some caps are not ties.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both conclusions I and II follow
A “possibility” conclusion follows if it is true in at least one diagram that fits the statements; an ordinary conclusion must be true in every such diagram.
“No belt is a tie”: the circles of belts and ties do not touch
“No tie is a cap”: the circles of ties and caps do not touch; nothing is said about belts and caps
Conclusion I: All belts being caps is a possibility. — Follows. Nothing stops the belts lying inside the caps: the diagram fits both statements and in it all belts are caps.
Conclusion II: Some caps are not ties. — Follows. No tie is a cap, so no cap is a tie; there are caps, so some caps are not ties.