What does the logical connective "AND" imply about two statements?

The logical connective "AND" implies that both components of the statement must be true for the entire statement to be considered true. In logical terms, when two statements, say P and Q, are connected by "AND" (written as P AND Q), the overall statement holds true only when both P is true and Q is true. If either P or Q is false, then the entire statement fails to be true. This characteristic of the conjunction is fundamental in logic and is used widely in various mathematical and logical reasoning applications.

In contrast, other options describe different logical connectives or scenarios. For instance, if at least one must be true, that would refer to the "OR" connective. Saying that only one can be true fits the definition of an exclusive "OR." Lastly, saying there is no requirement for either to be true does not reflect the nature of the "AND" connective, as it directly contradicts its requirement for both statements to be true. Thus, the understanding that both statements must be true for the conjunction to be true affirms the correctness of the answer provided.