Definition
Logical connectives are operators that combine simple propositions into compound ones. In classical propositional logic, the standard set is negation ~P, conjunction P ∧ Q, disjunction P ∨ Q, implication P ⊃ Q, and biconditional P ≡ Q. Each has a fixed truth-table semantics specifying its value for each combination of input values.
Why it matters
How it works
Each connective is defined by its truth table. To check whether a complex formula is a tautology (true under every assignment), construct the truth table over all assignments to its atomic propositions and verify the formula is true in every row. For long formulas this is exponential; equivalence-preserving transformations (DNF, CNF) make checking more efficient.