A proposition is a statement that is either true or false. We combine propositions using logical connectives.
| Connective | Symbol | Name | True when |
|---|---|---|---|
| NOT | ¬p | Negation | p is false |
| AND | p ∧ q | Conjunction | Both true |
| OR | p ∨ q | Disjunction | At least one true |
| IF…THEN | p → q | Implication | Not (p true AND q false) |
| IFF | p ↔ q | Biconditional | p and q have same truth value |
Implication: p → q is false ONLY when p is true and q is false. "If it rains, the ground is wet" is NOT falsified by dry weather with no rain.
p → q (implication) is FALSE only when
p ↔ q (biconditional) is true when
A tautology is
Which connective corresponds to 'exclusive or'?
'If it is Sunday then there is no mail' — the hypothesis is