# MAT299 Chapter Notes - Chapter 1: Propositional Calculus, Peano Axioms, Natural Number

Chapter 1. Propositional Logic

• Propositional logic is a branch of logic dealing with manipulation, modification or concatenation of

statements to form more complex proposition, relationship between propositions, and how to derive

conclusion based on premises

• Terminal (atomic) proposition is represented by alphabet (i.e. A, B, ...) and, is declarative statement that

evaluates to True or False

• Logical operators are connectives that join terminal propositions to create composite proposition; they

include the following:

o AND (∧): returns true only if both inputs are true

o OR (∨): returns true if at least one of inputs is true

o NOT (¬): reverts truth value of input

o IF ... THEN (→): material implication

o ... IF AND ONLY IF (↔): material equivalence

o NOT BOTH ... AND ... (|): equivalent to NOT (... AND ...)

o NEITHER ... NOR ... ( ): equivalent to (NOT ...) AND (NOT ...)

• A proposition is either atomic, combination of atomic statements connected by the operators mentioned

above, or composite of propositions recursively formed based on the following rules: