 Since every supervaluation is a classical valuation, every classical tautology is supertrue under every valuation function in \(\mathbf{K}_3\). Supervaluationism is, however, not truth-functional with respect to supervalues. The supervalue of a disjunction, for example, does not depend on the supervalue of the disjuncts. Suppose \(a(p) = I\). Then \(a(\neg p) = I\) and \(v_{a'} (p\vee \neg p) = T\) for every supervaluation \(v_{a'}\) of \(v_a\). Whereas \((p\vee \neg p)\) is thus supertrue under \(v_a,p\vee p\) is not, because there are superassignments \(a'\) of \(a\) with \(a'(p) = F\). An argument against the charge that supervaluationism requires a non-truth-functional semantics of the connectives can be found in MacFarlane (2008) (cf. also other references given there).