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 sailor is a farmer.
2. All sailors are cooks.
Conclusions:
I. No cook is a farmer.
II. All cooks are sailors.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Neither conclusion I nor conclusion II 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.
“No sailor is a farmer”: the circles of sailors and farmers do not touch
“All sailors are cooks”: the circle of sailors lies inside the circle of cooks; the other cooks are not covered by the first statement
Conclusion I: No cook is a farmer. — Does not follow. Only the sailors are kept away from the farmers; the other cooks may be farmers, as in the diagram.
Conclusion II: All cooks are sailors. — Does not follow. “All sailors are cooks” cannot be turned round; in the diagram many cooks are not sailors.