Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. All hills are mountains.
2. No hill is a valley.
Conclusions:
I. Some mountains are not valleys.
II. No mountain is a valley.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 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.
“All hills are mountains”: the circle of hills lies inside the circle of mountains
“No hill is a valley”: the circles of hills and valleys do not touch; the rest of the mountains are not covered by this statement
Conclusion I: Some mountains are not valleys. — Follows. The hills are mountains, and no hill is a valley; so these mountains are not valleys.
Conclusion II: No mountain is a valley. — Does not follow. Only the hills are kept away from the valleys; the other mountains may be valleys, as in the diagram.
Conclusion I follows on its own, so “either I or II” does not apply.