If the statement ‘some plants are carnivorous’ is given as true, then which of…
2022
If the statement ‘some plants are carnivorous’ is given as true, then which of the following could be immediately inferred from it: (A) ‘All plants are carnivorous’ is undetermined (B) ‘All plants are carnivorous’ is true (C) ‘Some plants are not carnivorous’ is undetermined (D) ‘No plants are carnivorous’ is false Choose the correct answer from the options given below:
Answer: D. (A), (C), (D) only — ConceptA particular affirmative proposition, “Some S are P,” asserts only that the sets S and P have at least one common member. It does not determine whether…
- A.
(B), (C), (D) only
- B.
(B) and (C) only
- C.
(B) and (D) only
- D.
(A), (C), (D) only
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept
A particular affirmative proposition, “Some S are P,” asserts only that the sets S and P have at least one common member. It does not determine whether every S is P or whether some S lies outside P, but it directly contradicts “No S are P.”
Application
Let S be plants and P be carnivorous things. “Some plants are carnivorous” means that S ∩ P is nonempty.
Because at least one plant lies in P, the inner claim “No plants are carnivorous” is false. Statement (D) says exactly that this inner claim is false, so statement (D) is true.
The premise does not say that every plant lies in P. Hence “All plants are carnivorous” can be true in one model and false in another, so statement (A) is undetermined and statement (B) is not inferred.
The premise also does not say whether any plant lies outside P. Hence “Some plants are not carnivorous” can be true in one model and false in another, so statement (C) is undetermined.
Cross-check and contrast
Model 1: every plant is carnivorous. The premise remains true, while there is no non-carnivorous plant.
Model 2: one plant is carnivorous and another is not. The premise remains true, while the universal claim fails.
These two models establish the two “undetermined” classifications; in both models the no-overlap claim is false, making statement (D) true.
(B), (C), (D) only includes (B), although the premise leaves universal coverage open.
(B) and (C) only includes (B) and omits the true evaluation expressed by (D).
(B) and (D) only includes (B) and omits the undetermined particular-negative evaluation in (C).
(A), (C), (D) only collects the two undetermined classifications and the true evaluation that the no-overlap claim is false.
Result
Therefore, the immediately inferable set is (A), (C), (D) only.