Complementary statements about wealth and poverty: From 'No gentleman is poor' and 'All gentlemen are rich', decide whether the conclusions (I) 'No poor man is rich' and (II) 'No rich man is poor' necessarily follow.

Given data

• Premise 1: Gentleman ∩ Poor = ∅.
• Premise 2: Gentleman ⊆ Rich.
• Conclusions: (I) No Poor is Rich. (II) No Rich is Poor.

Concept/Approach

The premises restrict relations involving the subset 'Gentleman', not the entire sets 'Rich' or 'Poor'. Without information about non-gentlemen, we cannot generalize to all rich or all poor.

Step-by-step evaluation

Verification/Alternative

Countermodel: Let Gentlemen = {g1}, Rich = {g1, r2}, Poor = {r2}. Premises hold (g1 rich, not poor), yet (I) is false (r2 is both rich and poor in a definitional sense) and (II) is false. Therefore no conclusion is necessary.

Common pitfalls

• Overextending results from a subset (Gentleman) to the whole set (Rich/Poor).

Final Answer
Neither I nor II follows.