Introduction / Context:
This question tests careful reading of universal negatives alongside a 'some' statement. We must avoid drawing unwarranted converses and overgeneralizations.
Given Data / Assumptions:
- M ∩ S = ∅ (no man is sky)
- S ∩ R = ∅ (no sky is road)
- ∃ element in M ∩ R (some men are roads)
Concept / Approach:
Disjointness is symmetric, so from 'No sky is road' we can also say 'No road is sky' (II). But a particular overlap between men and roads refutes any universal separation of roads from men.
Step-by-Step Solution:
II: No road is sky. This follows immediately from 'No sky is road' (disjointness is mutual).I: No road is man. False because we are given some men are roads.III: Some skies are men. False because no man is sky.IV: All roads are men. Not forced; we know some roads are men, but not necessarily all.
Verification / Alternative check:
A quick model: pick one element that is both man and road. Keep sky disjoint from both men and roads. Then only II holds. Since there is no option that states 'Only II follows', the correct meta-answer is 'None of these' among the provided choices.
Why Other Options Are Wrong:
A: Claims none follow; II clearly follows.B, C, D: Each includes at least one false conclusion (I and/or III) or omits the exact needed combination.
Common Pitfalls:
Forgetting symmetry of disjointness; confusing 'some' with 'all'; assuming a universal without textual support.
Final Answer:
None of these
Discussion & Comments