If ‘some men are vegetarians’ is given as false, which of the following can be…
2022
If ‘some men are vegetarians’ is given as false, which of the following can be inferred to be true from it?
(A) All men are vegetarians.
(B) No men are vegetarians.
(C) Some men are not vegetarians.
(D) All non-vegetarians are men.
Choose the correct answer from the options given below:
Answer: C. B and C Only — ConceptA categorical proposition states a relation between a subject class and a predicate class. The negation of the existential claim “Some S are P” is the…
- A.
A, B and C Only
- B.
B, C and D Only
- C.
B and C Only
- D.
C Only
Attempted by 6 students.
Show answer & explanation
Correct answer: C
Concept
A categorical proposition states a relation between a subject class and a predicate class. The negation of the existential claim “Some S are P” is the universal exclusion “No S are P”. In the traditional square of opposition used in such questions, universal propositions carry existential import, so “No S are P” also supports “Some S are not P”.
Application
The statement “Some men are vegetarians” is given as false. Therefore, there is no person who is both a man and a vegetarian.
This is exactly statement B: “No men are vegetarians.” Hence B is true.
Under existential import, men exist; since no man is vegetarian, at least one man is not vegetarian. Therefore statement C is also true.
Statement A contradicts B, and statement D reverses the subject-predicate direction, which does not follow from B.
Cross-check
Using symbols, false(∃x[M(x) ∧ V(x)]) gives ∀x[M(x) → ¬V(x)]. With ∃x M(x), this yields ∃x[M(x) ∧ ¬V(x)]. Thus B and C, and only B and C, follow.
Result: B and C only.