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 jockeys are riders.
2. Some jockeys are not tourists.
Conclusions:
I. Some riders are not tourists.
II. Some tourists are not jockeys.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 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. “Some X are not Y” cannot be read the other way round.
“All jockeys are riders”: the circle of jockeys lies inside the circle of riders
“Some jockeys are not tourists”: part of the jockeys lies outside the tourists
Conclusion I: Some riders are not tourists. — Follows. The jockeys who are not tourists are riders too, because every jockey is a rider; so these riders are not tourists.
Conclusion II: Some tourists are not jockeys. — Does not follow. The tourists may all be jockeys, as in the diagram; “some jockeys are not tourists” cannot be read the other way round.