If the statement, ‘Some officers are not honest’ is given as false, then which of the following statements can be inferred to be true?
A. All honest beings are officers
B. Some officers are honest
C. No officers are honest
D. All officers are honest
Choose the correct answer from the options given below:

Correct option is D

The given statement, "Some officers are not honest," is a particular negative (O form) proposition. If this statement is false, it means that all officers are honest (D) must be true. This is because the negation of a particular negative implies a universal affirmative, i.e., no officers are dishonest, which means all officers are honest. Additionally, from "All officers are honest," we can infer that some officers are honest (B), since "some" is included in "all." Thus, both B and D are true, while A and C cannot be inferred.
Information Booster:
1. The O form (Some S are not P) is a particular negative proposition.
2. The negation of an O proposition leads to an A proposition (All S are P), a universal affirmative.
3. If "Some officers are not honest" is false, then the opposite universal affirmative "All officers are honest" becomes true.
4. From "All officers are honest," we can infer the particular affirmative "Some officers are honest."