In the question below, two statements are followed by two conclusions, I and…
2022
In the question below, two statements are followed by two conclusions, I and II. Treat the statements as true even if they differ from commonly known facts. Study the conclusions carefully and decide which conclusion logically follows from the statements.
Statements
All cakes are desks.
All desks are toffees.
Conclusions
Conclusion I: All toffees are cakes.
Conclusion II: Some toffees are cakes.
Answer: B. Only conclusion II follows — Concept In a syllogism, if every A is B and every B is C, then every A is C. A universal statement cannot be reversed: A contained in C does not imply C…
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Both conclusions I and II follow
- D.
Neither conclusion I nor conclusion II follows
Attempted by 284 students.
Show answer & explanation
Correct answer: B
Concept
In a syllogism, if every A is B and every B is C, then every A is C. A universal statement cannot be reversed: A contained in C does not imply C contained in A. In this exam convention, a universal affirmative premise also carries existential import for the named class.
Application
Represent the statements as Cakes contained in Desks and Desks contained in Toffees.
By transitivity, Cakes are contained in Toffees.
Conclusion I reverses this relation to Toffees contained in Cakes, which the statements do not establish.
With the exam convention of existential import, cakes exist; because every cake is a toffee, some toffees are cakes. Thus conclusion II follows.
Cross-check
Imagine one cake inside the set of desks, with the desks inside the set of toffees, and an extra toffee outside the cake set. This arrangement satisfies both statements, makes conclusion I false, and makes conclusion II true.
Result: Only conclusion II follows.