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 cup is a plate.
2. Some plates are designs.
3. All designs are glasses.
Conclusions:
I. Some designs are not cups.
II. Some cups are glasses.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only conclusion I follows
A conclusion follows only if it is true in every diagram that fits the statements. One diagram in which a conclusion is false is enough to reject it.
“No cup is a plate”: the circles of cups and plates do not touch
“Some plates are designs”: the circles of plates and designs overlap
“All designs are glasses”: the circle of designs lies inside the circle of glasses; nothing is said about cups and glasses
Conclusion I: Some designs are not cups. — Follows. The designs that are plates can never be cups, because no plate is a cup.
Conclusion II: Some cups are glasses. — Does not follow. No statement links cups with glasses; the cups may lie wholly outside the glasses, as in the diagram.