In classical square of opposition if ‘No S is P’ is given as false then which…
2022
In classical square of opposition if ‘No S is P’ is given as false then which of the following could be immediately inferred from it?
(A) ‘Some S is not P’ is true
(B) ‘All S is P’ is undetermined
(C) ‘Some S is not P’ is undetermined
(D) ‘Some S is P’ is true
(E) ‘Some S is not P’ is false
Choose the correct answer from the options given below :
Answer: D. (B), (C) and (D) only — ConceptIn the classical square of opposition, A and O are contradictories, and E and I are contradictories. Contradictory propositions always have opposite…
- A.
(B), (C) and (E) only
- B.
(A), (B) and (D) only
- C.
(A), (D) and (E) only
- D.
(B), (C) and (D) only
Show answer & explanation
Correct answer: D
Concept
In the classical square of opposition, A and O are contradictories, and E and I are contradictories. Contradictory propositions always have opposite truth values. A and E are contraries, so the falsity of one does not determine the other.
Application
The proposition “No S is P” is the E-form.
The I-form “Some S is P” contradicts E. Therefore, when E is false, “Some S is P” is true.
The A-form “All S is P” is contrary to E. Since both contraries may be false, E being false leaves A undetermined.
The O-form “Some S is not P” is not the contradictory of E. E being false therefore leaves O undetermined.
Cross-check and contrast
Assigning “Some S is not P” both an undetermined status and a false status gives one proposition two statuses.
Assigning “Some S is not P” a true status does not follow from the falsity of E.
Assigning “Some S is not P” both true and false is internally inconsistent.
Leaving “All S is P” and “Some S is not P” undetermined while taking “Some S is P” as true follows the three relevant relations.
Hence, the immediate inferences are: “All S is P” is undetermined, “Some S is not P” is undetermined, and “Some S is P” is true.