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

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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
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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:
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