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 pens are wallets.
2. Some wallets are tables.
3. Some tables are circles.
4. Some circles are buses.
Conclusions:
I. Some buses are tables.
II. Some circles are wallets.
III. Some circles are pens.
IV. Some buses are wallets.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → None of the conclusions follows
Two “some” statements that share a class give no link between their other two classes: the part of wallets that is pens and the part of wallets that is tables may be different wallets. So in a chain of “some” statements, only classes that are next to each other in the chain are sure to meet.
The statements link pens–wallets, wallets–tables, tables–circles and circles–buses
The diagram draws each class meeting only its neighbours in this chain; it fits all four statements
Conclusion I: Some buses are tables. — Does not follow. Buses and tables are joined only through circles; in the diagram they do not meet.
Conclusion II: Some circles are wallets. — Does not follow. Circles and wallets are joined only through tables; in the diagram they do not meet.
Conclusion III: Some circles are pens. — Does not follow. Circles and pens are joined only through wallets and tables; in the diagram they do not meet.
Conclusion IV: Some buses are wallets. — Does not follow. Buses and wallets are joined only through circles and tables; in the diagram they do not meet.