Syllogism — Premises: P) All men are women. Q) All women are crazy. Conclusions: I) All men are crazy. II) All the crazy are men. III) Some of the crazy are men. IV) Some of the crazy are women.
-
ANone of the conclusions follows
-
BAll the conclusions follow
-
COnly I, III and IV follow
-
DOnly II and III follow
-
ENone of these
Answer
Correct Answer: Only I, III and IV follow
Explanation
Introduction / Context:Two universal inclusions form a chain: Men ⊆ Women ⊆ Crazy. We test which conclusions necessarily follow in standard syllogistic settings common to reasoning exams.
Given Data / Assumptions:
- P: Men ⊆ Women.
- Q: Women ⊆ Crazy.
- Routine assumption: the categories referenced (women, men) are not empty in ordinary-language reasoning problems.
Concept / Approach:From chained subsets, we get Men ⊆ Crazy (I). The statement II claims the converse of Women ⊆ Crazy and is not supported. Statements III and IV are existential claims that follow if the relevant categories have at least one member.
Step-by-Step Solution:
I) Men ⊆ Crazy follows by transitivity: Men ⊆ Women and Women ⊆ Crazy.II) 'All crazy are men' is converse and does not follow; there can be crazy individuals who are not men.III) 'Some crazy are men' holds if any man exists since Men ⊆ Crazy.IV) 'Some crazy are women' holds if any woman exists since Women ⊆ Crazy.Verification / Alternative check:Construct any world with at least one woman and one man; then I, III, IV are true while II can be false if there exist crazy persons who are not men.
Why Other Options Are Wrong:
- All follow: II fails.
- None follow: I certainly follows; III and IV follow under standard non-emptiness.
- Only II and III: II is wrong; IV also follows.
Common Pitfalls:Confusing universal subset with its converse; overlooking typical non-emptiness assumptions used in exam syllogisms.
Final Answer:Only I, III and IV follow.