Propositions and Connectives

A proposition is a declarative statement that has a truth value: true or false. Questions, commands, and open statements whose truth cannot yet be determined are not propositions in the same sense.

Read the connective as a relationship

• ∼P means not P.
• P ∧ Q means P and Q. Both parts must be true.
• P ∨ Q means P or Q, inclusively: at least one part is true.
• P → Q means if P, then Q. It is false only when P is true and Q is false.
• P ↔ Q means P if and only if Q. The two truth values must match.

A common translation trap is only if. “P only if Q” means P → Q: Q is required whenever P happens.

Use the Logic Basics lab to practice controlled examples before moving to full formulas.