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 ladders are tools.
2. All hammers are tools.
Conclusions:
I. Some ladders are hammers.
II. No ladder is a hammer.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Either conclusion I or conclusion II follows
When two conclusions do not follow on their own, but in every diagram exactly one of them is true (such as “some X are Y” and “no X is Y”), the answer is “either one or the other follows”.
“All ladders are tools”: the circle of ladders lies inside the circle of tools
“All hammers are tools”: the circle of hammers also lies inside the circle of tools; ladders and hammers may meet or may not
Conclusion I: Some ladders are hammers. — Does not follow on its own. In case 2 the ladders and hammers do not meet, so it is false there.
Conclusion II: No ladder is a hammer. — Does not follow on its own. In case 1 some ladders are hammers, so it is false there.
Ladders and hammers either meet or they do not; there is no third case. So in every diagram exactly one of I and II is true: either conclusion I or conclusion II follows.