Final answer:
The initial statement 'No A are non-B' means all A are B. Its conversion 'No B are non-A' does not necessarily maintain its truth value without context, since universal negative statements do not always convert truthfully.
Step-by-step explanation:
The original statement 'No A are non-B' is a categorical proposition. It means that there are no members of category A that are outside of category B. In other words, all A are B. Now let's consider the conversion of this statement, which would result in 'No B are non-A'. However, the conversion of universal negative statements (E propositions in traditional logic) do not necessarily maintain the truth value after conversion. Therefore, to assess the truth value of the converted statement we must examine the specifics of the sets A and B. Without additional context, we cannot determine the truth value of the converted statement.
For example, let’s consider the statement 'All dogs are mammals' (All A are B). This is true. However, the statement 'All mammals are dogs' (All B are A) is false. Similarly, from the statement 'No cats are non-mammals' (No A are non-B), we correctly infer that all cats are mammals, but we cannot conclude that no mammals are non-cats (No B are non-A).