Logical reasoning — Deductive facts (choose the statement that must be true) Facts: Jessica has four children. Two children have blue eyes and two have brown eyes. Half of the children are girls. Which of the following statements must also be a fact? I: At least one girl has blue eyes. II: Two of the children are boys. III: The boys have brown eyes.

Introduction / Context:
This question tests deductive reasoning from fixed facts about counts and categories. We must determine which follow-up statements are guaranteed to be true, not merely possible. Words like “must” signal logical necessity, so any statement that could be false under some valid arrangement is not a fact.

Given Data / Assumptions:

• Total children = 4.
• Eye color split: 2 blue, 2 brown.
• Sex split: half girls, hence 2 girls and (by arithmetic) 2 boys.
• No information links sex to eye color.

Concept / Approach:
Translate the counts into certain truths and then check each candidate statement. Any statement relying on an unprovided link (for example, tying eye color to sex) is not logically compelled. The goal is to see whether a statement is true in every arrangement that satisfies the facts.

Step-by-Step Solution:

Verification / Alternative check:
Construct two valid arrangements: (A) Boys = both blue, Girls = both brown (valid); (B) Boys = both brown, Girls = both blue (also valid). II holds in both arrangements; I and III do not hold in all arrangements. Hence only II must be true.

Why Other Options Are Wrong:

• I only: I is not guaranteed (counterexample A).
• II and III only: III is not guaranteed (counterexample A or B shows variability).
• None of the statements is a known fact.: Incorrect because II is a certainty.
• I and II only: I is not certain.

Common Pitfalls:
Assuming an unstated link between attributes (e.g., girls more likely to have a certain eye color). Counts alone cannot impose that link.

Final Answer:
II only