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 lockers are cabinets.
2. All cabinets are shelves.
3. No shelf is a drawer.
Conclusions:
I. Some lockers are not drawers.
II. No locker is a drawer.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 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 lockers are cabinets”: the circles of lockers and cabinets overlap; the rest of the lockers may lie anywhere
“All cabinets are shelves”: the circle of cabinets lies inside the circle of shelves
“No shelf is a drawer”: the circles of shelves and drawers do not touch
Conclusion I: Some lockers are not drawers. — Follows. The lockers that are cabinets are shelves, because every cabinet is a shelf, and no shelf is a drawer; so these lockers are not drawers.
Conclusion II: No locker is a drawer. — Does not follow. Only the lockers that are cabinets are kept away from the drawers; the other lockers may be drawers, as in the diagram.
Conclusion I follows on its own, so “either I or II” does not apply.