Step-by-step Solution:

Quick Solution

To solve this, we need to evaluate each of the three conclusions to see if they are guaranteed to be true based on the three initial statements (facts).

Evaluating the Conclusions

Let's analyze each conclusion one by one:

1. Conclusion I: "All birds lay eggs." The third fact states that "Female birds lay eggs." This tells us a property of a specific subset of birds, but it says nothing about male birds. We cannot generalize this to include *all* birds.
   Therefore, this conclusion is not necessarily true.
2. Conclusion II: "Some hens are birds." We are given two facts: "All chickens are birds" and "Some chickens are hens." If a creature is a chicken that is also a hen, and all chickens are a type of bird, then that specific hen must also be a bird. A Venn diagram confirms this: the "Chickens" circle is entirely inside the "Birds" circle, and the "Hens" circle must overlap the "Chickens" circle, meaning it also overlaps the "Birds" circle.
   Therefore, this conclusion is true.
3. Conclusion III: "Some chickens are not hens." In logical reasoning questions, the statement "Some A are B" is commonly interpreted to imply that "Not all A are B" (meaning there also exist some A's that are not B's).
   Given the fact "Some chickens are hens," and following this standard interpretation, it implies that the group of all chickens is not entirely composed of hens.
   Therefore, this conclusion is also considered true.

Conclusion

Based on the analysis:

• Conclusion I is false.
• Conclusion II is true.
• Conclusion III is true.

Final Answer: The statements that must also be a fact are II and III.