1. **State the problem:** We are given two statements and two conclusions, and we need to determine which conclusions logically follow from the statements. 2. **Analyze the statements:** - Statement i) "All dogs are cats" means the set of dogs is completely inside the set of cats. - Statement ii) "Some cats are black" means there is an overlap between the set of cats and the set of black things. 3. **Analyze Conclusion I: "Some dogs are black."** - Since all dogs are cats, any dog is a cat. - Some cats are black, but this does not guarantee that the dogs (which are a subset of cats) are black. - Therefore, Conclusion I does not necessarily follow. 4. **Analyze Conclusion II: "Some cats are dogs."** - Since all dogs are cats, the dogs are a subset of cats. - This means there are cats that are dogs (specifically, all dogs). - Therefore, Conclusion II logically follows. 5. **Final answer:** - Conclusion I does not follow. - Conclusion II follows. Hence, only Conclusion II is valid based on the given statements.