Propositional logic allows us to analyze arguments that depend on
logical relationships among compound propositions. The units of
analysis are component propositions along with the truth-functional connectives. However, some arguments require a finer-grained analysis. In some cases, we need to break propositions
down into their elements, and this is the function of predicate
First, we examine the symbolic notation used to represent
the inner structure of propositions. Then we present a few
new rules of inference and see how to use them along with the
propositional rules in constructing proofs.