If the statement 'All men are honest' is given as false. which of the following could be inferred immediately from it?
(A) "Some men are honest is false
(B) 'No men are honest' is true
(C) "No men are honest' is undetermined
(D) 'Some men are not honest' is true
Choose the correct answer from the options given below:

Correct option is B

If the statement 'All men are honest' is false, it implies that not all men are honest, meaning there are exceptions to the claim. Here's the reasoning for each option:
· (C) "No men are honest" is undetermined: Correct, because the falsity of "All men are honest" does not confirm or deny that "No men are honest."
· (D) "Some men are not honest" is true: Correct, as this directly follows from the falsity of "All men are honest." If all are not honest, at least some must not be honest.
Information Booster 1. Universal affirmative ('All men are honest'): Its negation implies the existence of at least some exceptions.
2. Contradictory propositions:
· "All men are honest" contradicts "Some men are not honest."
· "No men are honest" contradicts "Some men are honest."
3. Particular propositions ('Some men are honest' or 'Some men are not honest'): These may hold true independently of the universal statements.
4. Logical inference relies on the immediate scope of negation and cannot assume undetermined statements as true.
Additional knowledge
· (A) "Some men are honest" is false: Incorrect, as we cannot deduce this directly. If "All men are honest" is false, "Some men are honest" might still hold true, making it undetermined.
· (B) "No men are honest" is true: Incorrect, as "No men are honest" cannot be inferred from the falsity of "All men are honest." It is undetermined.