If the proposition 'All men are rich' is false, then which of the following prepositions can be claimed certainly to be true?

Proposition: "All men are rich" (False) 

If the proposition "All men are rich" is false, it means that it is not true that every single man is rich. Therefore, at least one man must not be rich

Option A: "Some men are not rich" - This can certainly be true because if not all men are rich, then at least some men must not be rich.

Option B: "No rich person is a man" - This cannot be claimed certainly to be true because it suggests that no man is rich, which is not necessarily implied by the original proposition being false.

Option C: "No man is rich" - This cannot be claimed certainly to be true because it implies that all men are not rich, which is not necessarily implied by the original proposition being false.

Option D: "Some men are rich" - This cannot be claimed certainly to be true because the original proposition being false doesn't provide enough information to conclude that some men are rich.

Thus, correct answer is (a) Some men are not rich