Step-by-Step Logical Analysis

To determine which conclusion must be a fact, we need to evaluate each one based on the three initial statements provided.

The Given Facts:

1. All chickens are birds.
2. Some chickens are hens.
3. Female birds lay eggs.

Evaluating the Conclusions:

I. All birds lay eggs.

• Analysis: Fact 3 states that only female birds lay eggs. It provides no information about male birds. Since the group "all birds" includes male birds, we cannot conclude that all of them lay eggs.
• Verdict: This statement is not necessarily a fact.

II. Some hens are birds.

• Analysis: Fact 2 tells us that there is a group of animals that are both chickens and hens. Fact 1 tells us that every single chicken is also a bird. Therefore, the group of animals that are chickens and hens must also be birds. This means there is a group of hens that are birds.
• Verdict: This statement must be a fact.

III. Some chickens are not hens.

• Analysis: Fact 2, "Some chickens are hens," only confirms that at least one chicken is a hen. It does not rule out the possibility that all chickens might be hens. In formal logic, "Some A are B" does not guarantee that "Some A are not B". Since we cannot be certain, this is not a guaranteed fact.
• Verdict: This statement is not necessarily a fact.

Conclusion

Based on the analysis, only Conclusion II logically follows from the given statements and must also be a fact.