Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. Some clerks are not typists.
2. All cashiers are typists.
Conclusions:
I. Some cashiers are not clerks.
II. Some clerks are not cashiers.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only conclusion II 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.
“Some clerks are not typists”: part of the clerks lies outside the typists
“All cashiers are typists”: the circle of cashiers lies inside the circle of typists; nothing is said about cashiers and clerks
Conclusion I: Some cashiers are not clerks. — Does not follow. The cashiers may all be clerks, as in the diagram.
Conclusion II: Some clerks are not cashiers. — Follows. The clerks who are not typists cannot be cashiers, because every cashier is a typist.
Conclusion II follows on its own, so “either I or II” does not apply.