Propositions

Compound Proposition

The combination of 2 or more simple propositions formed using logical connectors.

Simple Proposition

Propositions that cannot be broken down further.

Negation

The negation of proposition P is denoted by ~P, read as not P.

Conjunction

The conjunction of propositions P and Q is denoted by P^Q, read as P and Q.

Disjunction

The disjunction of propositions P and Q is denoted by PvQ, read as P or Q.

Conditional

The conditional of propositions P and Q is denoted by P → Q, read as if P then Q.

Biconditional

The biconditional of propositions P and Q is denoted by P <-> Q, read as P if and only if Q or P iff Q.

When is a statement considered a proposition?

When it’s a declaration and when you can prove if its true or false.

Converse

If q, then p

Inverse

If not q, then not p.

Contrapositive

if not p, then not q.