The questions below have four groups of three statements each. Read each group…
2024
The questions below have four groups of three statements each. Read each group and identify where the third statement logically follows from the first two.
Question 3
A) All books are copies. All copies are papers. All books are papers.
B) All cubes are squares. All cubes are triangles. All triangles are squares.
C) All singers are dancers. All dancers are musicians. All musicians are singers.
D) No cock is a hen. All hens are chickens. No hen is a chicken.
- A.
Only D
- B.
Only A
- C.
Only B and C
- D.
Only A and D
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept: Two categorical statements of the form ‘All X are Y’ and ‘All Y are Z’ chain by transitivity of set inclusion to give ‘All X are Z’ (X is a subset of Y, Y is a subset of Z, therefore X is a subset of Z). This chaining is valid only when the two premises link through a shared middle term in the same subject-to-predicate direction — reversing that direction, connecting two predicates that merely share a common subject, or drawing a conclusion that contradicts one of the premises all break the syllogism.
Application:
Group | Premises | Claimed third statement | Valid? |
|---|---|---|---|
A | Books are a subset of Copies; Copies are a subset of Papers | Books are a subset of Papers | Valid — a direct transitive chain. |
B | Cubes are a subset of Squares; Cubes are a subset of Triangles | Triangles are a subset of Squares | Invalid — both premises share the same subject (Cubes); that never fixes a relation between the two predicates. |
C | Singers are a subset of Dancers; Dancers are a subset of Musicians | Musicians are a subset of Singers | Invalid — the valid chain runs Singers to Musicians; the stated conclusion reverses that direction. |
D | No Cock is a Hen; Hens are a subset of Chickens | No hen is a chicken | Invalid — directly contradicts the premise that all hens are chickens. |
Cross-check: A quick counter-example confirms each verdict. For Group B, picture Squares and Triangles as two separate circles that both simply contain the Cubes circle — nothing forces one of them to contain the other. For Group C, someone can belong to Musicians without belonging to Singers, so the reverse inclusion does not hold. For Group D, since every hen already belongs to Chickens by the premise, no hen can simultaneously fall outside Chickens.
Only Group A's third statement is a valid logical consequence of its premises, so the correct choice is the one stating Only A.
