Is the logical system that studies relationships between sentences. atomic sentences are the basic units in this logical system. they can be combined in more complex sentences by means of logical connectives?

The answer is Propositional logic or Sentential logic.

This type of logic is aimed to anlyze how to combine statements, prepoisitions, and sentences by using logical connectives.

By using this logic, we could expressed the sentence in a way that we could determine whether the sentence is true or false.