# Propositional logic

Propositional logic

system of logic that evaluates the validity of arguments using statements translated from ordinary language into symbols and logical operators

Simple statements

does not contain any operators

Compound statements

contains at least one simple statement and at least one logical operator

Negation

Uses the tilde (~) which goes before the letter representing the simple statement

Conjunction

Uses the dot symbol (�)
Used for words or phrases such as "and", "but", "moreover", "yet", "although", "whereas

Disjunction

Uses the wedge symbol (v)
Used for words or phrases such as "or", "either...or...", "whether...or...", "unless"*, "neither...nor...

Exclusive disjunction

at least one of the disjuncts is true, but not both

Inclusive disjunction

At least one disjunct is true, and possibly both are true

Conditional Statements

If...then...
Uses the horseshoe (?)
If antecedent, then consequent; Consequent if antecedent

Antecedent

statement that comes after "if" (or equivalent word)

Consequent

statement that comes after "then

Biconditional Statements

Used for the phrase "if and only if"
The truth of one of the statements is entirely dependent upon the truth of the other statement, and vice versa

Truth table

study truth table