If the statement, 'Some officers are not honest' is given as false, then which…

Concept

Categorical propositions are paired on the traditional square of opposition. An O-proposition (“Some S are not P”) and the corresponding A-proposition (“All S are P”) are contradictories: if one is false, the other is true.

Under the traditional existential-import assumption used in these questions, a true A-proposition subalternates to the corresponding I-proposition (“Some S are P”).

Application

1. Classify “Some officers are not honest” as an O-proposition and use the given information that it is false.

2. Its contradictory A-proposition, “All officers are honest,” must therefore be true.

3. By subalternation with existential import, “Some officers are honest” is also true.

Cross-check and contrast

• “B only” includes the particular affirmative consequence but omits the contradictory universal conclusion.

• “D only” includes the contradictory universal conclusion but omits its particular subaltern.

• “A and C only” reverses the subject–predicate direction in A and asserts the E-proposition in C, so it does not preserve the required square-of-opposition relations.

Therefore both “Some officers are honest” and “All officers are honest” follow, so the valid combination is “B and D only.”