If all cats are mammals, and some mammals are black, which of the following statements must be true?

To analyze the logical implications of the given statements, we can break it down and discuss the reasoning.

1. Premises:

   • All cats are mammals.
   • Some mammals are black.

2. Logical Deduction:

   • Since all cats belong to the group of mammals, it implies that if a cat exists, it is a mammal.
   • However, the fact that some mammals are black does not imply that cats must be black or that all mammals are black. It simply indicates that within the group of mammals, there is a subset that is black.

3. Conclusions:

   • Because there is no direct indication that all mammals or specifically all cats are black based on the premises, we cannot definitively state that all cats or any specific cat must be black.

Therefore, the statements that can be inferred must include the understanding that while all cats are mammals, they may not necessarily be black, and only some mammals are black.

Summary:

The premises suggest that while there is a relationship between cats and mammals, additional specific information regarding the coloration of cats cannot be conclusively drawn from the statements provided. Hence, while it is true that all cats are mammals, we cannot definitively state anything about their coloration from the information given.