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 balloons are hats.
2. All hats are cakes.
Conclusions:
I. All cakes are balloons.
II. All balloons are cakes.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Neither conclusion I nor conclusion II follows
A conclusion follows only if it is true in every diagram that fits the statements. An “all” conclusion needs one whole circle to lie inside another in every such diagram.
“Some balloons are hats”: the circles of balloons and hats overlap
“All hats are cakes”: the circle of hats lies inside the circle of cakes; the balloons outside the hats may lie outside the cakes
Conclusion I: All cakes are balloons. — Does not follow. Nothing puts the whole circle of cakes inside the balloons; in the diagram many cakes are not balloons.
Conclusion II: All balloons are cakes. — Does not follow. Only the balloons that are hats must be cakes; the other balloons may lie outside the cakes, as in the diagram.