ABSTRACT
The existence of a propositional variable both negated and unnegated is a sufficient condition for the validity of a purely disjunctive wff. It is, in fact, also a necessary condition. For unless it is satisfied it will always be possible to find an assignment of truth-values to the variables under which the whole wff turns out to be false. To avoid having to make special cases of certain types of wff, introduces the notion of a degenerate conjunction. A wff is a degenerate conjunction if it could appear as one conjunct in the sense of conditions. Then ‘conjunction’ and ‘disjunction’ in those conditions are taken to include the degenerate cases. Therefore the disjunction of them all must be valid. Therefore any disjunction which contains them all among its disjuncts must be valid.
