Syllogism reasoning practice: evaluate the categorical statements 'All men are dogs' and 'All dogs are cats' to decide which conclusion(s) necessarily follow (i) All men are cats, (ii) All cats are men — detailed logic with set–subset analysis

Given data

• Premise 1: All men are dogs (Men ⊆ Dogs).
• Premise 2: All dogs are cats (Dogs ⊆ Cats).
• Conclusions to test: (I) All men are cats; (II) All cats are men.

Concept/Approach (why this method)

Use transitivity of subset relations in categorical syllogisms: if A ⊆ B and B ⊆ C, then A ⊆ C. Beware of reversing arrows (the converse need not hold).

Step-by-Step calculation (logical derivation)
1) From Premise 1 and Premise 2, chain the inclusions: Men ⊆ Dogs ⊆ Cats.2) Therefore Men ⊆ Cats ⇒ Conclusion I is necessarily true.3) 'All cats are men' would require Cats ⊆ Men, which is not implied. Hence Conclusion II is false.

Verification/Alternative

Venn sketch: put the Men circle inside Dogs, and Dogs inside Cats. The diagram validates (I) and contradicts (II).

Common pitfalls

• Affirming the converse: assuming Cats ⊆ Men from Men ⊆ Cats.
• Forgetting that universal statements do not automatically reverse.

Final Answer
Only conclusion I follows.