Question

Explain the difference between propositional variable and propositional constant.

Answer 1

Propositional logic is an axiomatization of Boolean logic. As such predicate logic includes propositional logic. Both systems are known to be consistent, e.g. by exhibiting models in which the axioms are satisfied.

and "complete" in that every tautology in the sentential calculus (basically a Boolean expression on variables that represent "sentences", i.e. that are either True or False) can be proven in propositional logic (and conversely).

Predicate logic (also called predicate calculus and first-order logic) is an extension of propositional logic to formulas involving terms and predicates