Disjunction is the combination of two sentences with or. In propositional logic, the disjunction of two formulas phi and psi, written phi v psi, is true if phi is true or psi is true or both, as is shown in the truth-table (i):
(i) phi psi phi v psi 1 1 1 1 0 1 0 1 1 0 0 0
This version of disjunction is called inclusive, because it allows the propositions phi and psi both to be true. Natural language or can also be used exclusively: only one of the two propositions may be true, but not both (either ... or ...).
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.