Syllogism — Women, cats, and rats (subset chaining): Statements: • All women are cats. • All cats are rats. Conclusions: I. All women are rats. II. All rats are women.

Introduction / Context:Another transitivity check with attention to the direction of inclusion.

Given Data / Assumptions:

• Woman ⊆ Cat.
• Cat ⊆ Rat.

Concept / Approach:Chain inclusions to get Woman ⊆ Rat (I true). II reverses inclusion and is not warranted.

Step-by-Step:1) Woman ⊆ Cat and Cat ⊆ Rat.2) Hence Woman ⊆ Rat (I follows).3) “All rats are women” would require Rat ⊆ Woman, which is not implied.

Verification:Consider many rats that are not cats; premises do not forbid them.

Final Answer:Only conclusion I follows.