Syllogism with two independent properties — horns and lights on taxis Statements: • Some taxis have horns. • Some taxis have lights. Conclusions to evaluate: I. Every taxi has either a horn or a light. II. Some taxis have neither a light nor a horn. III. Some taxis have both horns and lights. IV. No taxi has both a horn and a light.

Introduction / Context:
This question examines reasoning about existence with two independent features on the same class (taxis). The premises say at least one taxi has a horn and at least one taxi has a light, but they do not specify whether any taxi has both or whether some have neither.

Given Data / Assumptions:

• T = set of taxis, H = taxis with horns, L = taxis with lights.
• H is nonempty; L is nonempty.
• No other restrictions on H and L are given.

Concept / Approach:
From the premises alone, two mutually exclusive possibilities remain about the intersection H ∩ L: either it is nonempty (at least one taxi has both features) or it is empty (no taxi has both). Logic guarantees that exactly one of these two possibilities must be true. However, nothing forces every taxi to have at least one feature or guarantees that some taxis have neither.

Step-by-Step Solution:

Verification / Alternative check:
Model A: One taxi is both horned and lighted (intersection nonempty) shows III true and IV false. Model B: Different taxis separately carry horn and light with no overlap shows III false and IV true. In both models, I and II remain unforced.

Why Other Options Are Wrong:

• Pairs like I and II / II and III / II and IV: each asserts non-necessary claims.
• All follow: clearly false since I and II are not guaranteed.

Common Pitfalls:
Assuming that some in both features implies there is a taxi with both; assuming every taxi must have at least one highlighted feature.

Final Answer:
Either III or IV follows