We have thus five functions: negation, disjunction, conjunction, incompatibility, and implication. We might have added others, for example, joint falsehood, "not-
and not-
," but the above five will suffice. Negation differs from the other four in being a function of one proposition, whereas the others are functions of two. But all five agree in this, that their truth-value depends only upon that of the propositions which are their arguments. Given the truth or falsehood of
, or of
and