Syllogism — Cows, chairs, and tables: Statements: (A) No cow is a chair. (B) All chairs are tables. Conclusions to test: I. Some tables are chairs. II. Some tables are cows. III. Some chairs are cows. IV. No table is a cow. Select the correct option.

Difficulty: Medium

Correct Answer: Only I follows

Explanation:


Introduction / Context:
This classic syllogism mixes a universal negative (No A are B) with a universal affirmative subset relation (All B are C). We must determine which conclusions are logically compelled without assuming information not given.


Given Data / Assumptions:

  • (A) No cow is a chair (Cow ∩ Chair = ∅).
  • (B) All chairs are tables (Chair ⊆ Table).


Concept / Approach:
Map sets: Cow (Cw), Chair (Ch), Table (Tb) with Ch ⊆ Tb and Cw ∩ Ch = ∅. Evaluate each conclusion.


Step-by-Step Solution:
1) From (B), if chairs exist, those chairs are tables; hence “Some tables are chairs” is accepted in test convention (Conclusion I follows).2) II “Some tables are cows” has no support; nothing links tables (in general) to cows.3) III “Some chairs are cows” contradicts (A) and is false.4) IV “No table is a cow” overreaches: (A) only forbids cows from being chairs, not from being other kinds of tables.


Verification / Alternative check:
Let chairs exist and be a subset of tables; let cows be disjoint from chairs; allow tables that are not chairs. Only I is forced.


Why Other Options Are Wrong:
(a) and (b) include false parts; (d) is impossible; (e) fails because I does follow.


Common Pitfalls:
Converting “All B are C” to “All C are B,” or projecting disjointness beyond what is stated.


Final Answer:
Only I follows.

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