How did Carnap connect the meaning of a sentence with its truth conditions?

In the context of metalogic, Rudolf Carnap connected the meaning of a sentence to its truth conditions by utilizing a formal semantic approach.

Within a formal language, Carnap proposed that one could define a notion of truth that establishes the necessary and sufficient conditions for a sentence to be true. He identified the meaning of a sentence with these conditions, asserting that to understand a sentence—or to know what it asserts—is equivalent to knowing the conditions under which it would be true.1

This framework relies on the concept of the logical range of a sentence, which is defined as the set of all possible worlds in which that sentence is true. By knowing these conditions, one possesses the necessary starting point for determining the sentence's actual truth-value. This method allowed Carnap to provide a rigorous, formal treatment of meaning, distinguishing it from mere confirming evidence, which had previously led to philosophical confusion in areas like logical positivism.123