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:.

Question

Solve this multiple-choice question and choose the correct option.

Curioustab · Accepted Answer

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: I: “All birds lay eggs.” The premise restricts egg-laying to female birds, so not all birds (males exist). I is false.II: “Some hens are birds.” From “Some chickens are hens” and “All chickens are birds,” those hens are birds. II must be true.III: “Some chickens are not hens.” “Some chickens are hens” does not imply others are not; it is compatible with all chickens being hens. III is not guaranteed. 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

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.

Answer

Explanation