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 judges are readers.
2. All judges are travellers.
3. Some writers are not readers.
Conclusions:
I. Some readers are travellers.
II. Some writers are not judges.
III. Some travellers are not writers.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only conclusions I and II follow
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. “Some X are not Y” cannot be read the other way round.
“All judges are readers”: the circle of judges lies inside the circle of readers
“All judges are travellers”: the circle of judges also lies inside the circle of travellers
“Some writers are not readers”: part of the writers lies outside the readers; the rest of the writers may lie anywhere, even over all the readers and travellers
Conclusion I: Some readers are travellers. — Follows. The judges are readers and also travellers, so at least the judges are readers who are travellers.
Conclusion II: Some writers are not judges. — Follows. The writers who are not readers cannot be judges, because every judge is a reader.
Conclusion III: Some travellers are not writers. — Does not follow. The writers may cover all the travellers, as in the diagram; then every traveller is a writer.