Accept every statement below as true, whatever the real world says. Which of the conclusions must then be true?
Statements:
1. No demand is a pencil.
2. All demands are claims.
Conclusions:
I. No pencil is a claim.
II. All claims are demands.
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. One diagram in which a conclusion is false is enough to reject it.
“All demands are claims”: the circle of demands lies inside the circle of claims
“No demand is a pencil”: the circle of pencils keeps away from the demands, but it may still overlap the claims outside the demands
Conclusion I: No pencil is a claim. — Does not follow. In the diagram the pencil circle overlaps the claims outside the demands, so some pencils are claims.
Conclusion II: All claims are demands. — Does not follow. “All demands are claims” cannot be reversed: the claims outside the demand circle are not demands.
The two conclusions do not cover every case between them (in the diagram both are false), so “either I or II” does not apply.