Logical reasoning — Hats, colors, and caps (choose the statement that must be true) Facts: All hats have brims. There are black hats and there are blue hats. Baseball caps are hats. Which statements must also be facts? I: All caps have brims. II: Some baseball caps are blue. III: Baseball caps have no brims.

Introduction / Context:
This is a classic test of careful reading and scope. We are told about “hats” in general and “baseball caps” in particular, plus the existence of hats in two colors. We must avoid making leaps from “baseball caps” to “all caps,” or from existence of blue hats to existence of blue baseball caps.

Given Data / Assumptions:

• All hats have brims.
• Existence: there are black hats and blue hats (not necessarily baseball caps).
• Baseball caps are hats.

Concept / Approach:
Check whether each candidate statement is guaranteed by the premises without adding assumptions. In particular, watch out for category shifts (caps in general vs. baseball caps) and contradictions with given universals.

Step-by-Step Solution:

Verification / Alternative check:
Construct a consistent model where all blue hats are fedoras (not baseball caps). Then II fails, I remains unproven, and III contradicts the premises. Hence none of I–III is a must.

Why Other Options Are Wrong:

• I only / II only / II and III only / I and II only: Each asserts at least one statement that is not guaranteed.

Common Pitfalls:
Assuming “caps” always means “hats,” and inferring color membership of subtypes from color existence in the larger group.

Final Answer:
None of the statements is a known fact.