MAT299 Chapter Notes - Chapter 1: Propositional Calculus, Peano Axioms, Natural Number
17 May 2020
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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:
