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 trays are boxes.
2. All boxes are crates.
3. No crate is a sack.
Conclusions:
I. Some trays are not sacks.
II. No tray is a sack.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 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 trays are boxes”: the circles of trays and boxes overlap; the rest of the trays may lie anywhere
“All boxes are crates”: the circle of boxes lies inside the circle of crates
“No crate is a sack”: the circles of crates and sacks do not touch
Conclusion I: Some trays are not sacks. — Follows. The trays that are boxes are crates, because every box is a crate, and no crate is a sack; so these trays are not sacks.
Conclusion II: No tray is a sack. — Does not follow. Only the trays that are boxes are kept away from the sacks; the other trays may be sacks, as in the diagram.
Conclusion I follows on its own, so “either I or II” does not apply.