Syllogism trap with partial information: 'All artists are smokers' and 'Some smokers are drunkards' — determine whether it follows that all smokers are artists or that some drunkards are not smokers

Given data

• Premise 1: All artists are smokers (Artists ⊆ Smokers).
• Premise 2: Some smokers are drunkards (∃ Smokers ∩ Drunkards).
• Conclusions: (I) All smokers are artists. (II) Some drunkards are not smokers.

Concept/Approach (why this method)

Do not invert subsets; also, 'Some smokers are drunkards' gives existence of overlap, not any element outside Smokers.

Step-by-Step calculation (logical derivation)
1) From Premise 1, Smokers may include non-artists; thus 'All smokers are artists' is invalid.2) Premise 2 states there exists at least one person who is both a smoker and a drunkard; it does not assert any drunkard outside Smokers.3) Therefore II ('Some drunkards are not smokers') is not compelled.

Verification/Alternative

Construct a model: let Artists ⊆ Smokers; pick one element in Smokers ∩ Drunkards; no drunkard outside Smokers is needed to satisfy premises.

Common pitfalls

• Converse error in (I).
• Inferring negatives ('not') from a mere positive intersection.

Final Answer
Neither I nor II follows.