Logical reasoning — Birds and chickens (choose the statement that must be true) Facts: All chickens are birds. Some chickens are hens. Female birds lay eggs. Which statements must also be facts? I: All birds lay eggs. II: Some hens are birds. III: Some chickens are not hens.

Introduction / Context:
We are asked to deduce guaranteed truths from basic category statements about chickens, birds, and egg-laying. The key is to apply subset logic and avoid overgeneralizing “some” to “all.”

Given Data / Assumptions:

• C ⊆ B (all chickens are birds).
• Some C are hens.
• Only female birds lay eggs (stated as “Female birds lay eggs”).

Concept / Approach:
From “some chickens are hens,” we know there exists at least one chicken that is a hen. Because all chickens are birds, that hen is also a bird. However, we cannot infer anything about all birds from a statement about female birds, and we cannot deduce the existence of non-hen chickens just from “some chickens are hens.”

Step-by-Step Solution:

Verification / Alternative check:
Create two consistent models: (A) All chickens are hens; (B) Only some chickens are hens. Statement II holds in both; I and III fail in at least one model, so only II is necessary.

Why Other Options Are Wrong:

• I only: I overgeneralizes the egg-laying condition.
• II and III only / I and II only: III is not forced; I is false.
• None of the statements is a known fact.: Incorrect because II is certain.

Common Pitfalls:
Confusing “some” with “not all,” and misreading a statement about female birds as a statement about all birds.

Final Answer:
II only