Propositions and Connectives

Discrete Math · Axiom Academy

LESSON Propositions and Connectives The foundation of formal logic: understanding propositions, logical operators, and how truth values combine to form compound statements. Propositions are the atomic units of logic. We typically use letters like p , q , and r to represent them. Each proposition has exactly one truth value. Connectives are operators that combine propositions to create compound statements. There are five fundamental connectives: The conjunction p ∧ q is true only when both p and q are true . If either proposition is false, the entire conjunction is false. The disjunction p ∨ q is true when at least one of p or q is true . It's false only when both are false. This is inclusive OR . 5. Implication (IF-THEN): p → q The implication p → q (read "if p then q") is false only when p is true but q is false . This is the most counterintuitive connective!

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