Propositional Logic

Proposition - A declarative sentence that states a fact or statement that results in either True or False

Logic Operators & Compound Propositions

Symbol	Name	Intuition
$\neg$	negation	not
$\wedge	conjunction	and
$\vee$	disjunction	or
$\to$	implication	if ... then
$\iff$	equivalence	if and only if
$\oplus$	exclusive	either
$\forall$	for all	all have to be true
$\exists$	there exists	at least one

More Terminology

Conditional Statement (if, then)
- $p \to q$ : " $p$ implies $q$ , if $p$ then $q$ "
Converse:
- $q \to p$
Contrapositive:
- $\neg q \to \neg p$
Inverse:
- $\neg p \to \neg q$
Biconditional
- $p \iff q$ : "p if and only iff q"

Discrete Mathematics