The difference between predicate and propositional logic and

The difference between predicate and propositional logic and giving examples of both propositional and predicate logic.

Solution

Propositional logic (also called sentential logic) is the logic the includes sentence letters (A,B,C) and logical connectives, but not quantifiers. The semantics of propositional logic uses truth assignments to the letters to determine whether a compound propositional sentence is true.

Predicate logic is usually used as a synonym for first-order logic, but sometimes it is used to refers to other logics that have similar syntax. Syntactically, first-order logic has the same connectives as propositional logic, but it also has variables for individual objects, quantifiers, symbols for functions, and symbols for relations. The semantics include a domain of discourse for the variables and quantifiers to range over, along with interpretations of the relation and function symbols.

Many undergrad logic books will present both propositional and predicate logic, so if you find one it will have much more info. A couple well-regarded options that focus directly on this sort of thing are Mendelson\'s book or Enderton\'s book.