Discrete Math

Proposition

Declared statement that is T/F but not both

Propositional variable

Variables used to denote propositions (usually p,q,r,s, but can be anything)

Truth value

The indication of whether a proposition is T/F

Compound propositions

Propositions formed by combining other propositions using logical operators

Negation

“It is not the case that p…”, read as not p

Conjunction

“p and q”

Disjunction

“p or q” (inclusive)

XOR

“p or q” (exclusive)

Implication/Conditional Statement

“if p then q”, “p implies q”, p → q

Converse

Flipping the propositions in a conditional statement creates the

Inverse

Negating both propositions in a conditional statement creates the

Contrapositive

Flipping and negating the propositions in a conditional statement creates the

Logical Equivalence

When 2 compound propositions always share the same truth values

Biconditional

“p if and only if q”, denoted as p ←→ q

Tautology

A proposition that is always True

Contradiction

A proposition that is always False

Contingency

A proposition that is neither a tautology or contradiction; it is contingent upon the truth values of the propositional inputs