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 pebbles are stones.
2. No stone is a shell.
3. No shell is a pearl.
Conclusions:
I. Some pebbles are pearls.
II. No pebble is a pearl.
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 pebbles are stones”: the circle of pebbles lies inside the circle of stones
“No stone is a shell”: the circles of stones and shells do not touch
“No shell is a pearl”: the circles of shells and pearls do not touch; nothing links the pearls with the pebbles
Conclusion I: Some pebbles are pearls. — Does not follow on its own. In case 2 the pebbles and pearls do not meet, so it is false there.
Conclusion II: No pebble is a pearl. — Does not follow on its own. In case 1 some pebbles are pearls, so it is false there.
Pebbles and pearls 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.