 Another system which rejects bivalence while validating LEM is supervaluationism (van Fraassen 1966). Let \(V\) be a set of classical valuations \(v\), where a classical valuation is a function assigning T(rue) or F(alse) to any statement in the relevant language. A supervaluation \(s_V\) is then a function assigning T (F) to exactly those statements assigned T (F) by all valuations in \(V\). Since \(V\) can contain classical valuations that assign different values to one and the same statement (e.g., if \(v_1(p)\)=T and \(v_2(p)=\)F for \(v_1,v_2 \in V\)), supervaluations have truth-value gaps (\(s_V(p)\) is undefined), so the law of bivalence fails. LEM, by contrast, is validated, since \(v(\phi \vee \neg \phi)\)=T for all \(\phi\) and classical \(v\), and thus \(s_V(\phi \vee \neg \phi)\) = T, for any \(s_V\). Thus, in supervaluationism, a disjunction can be supertrue (i.e., can be assigned T in some \(s_V\)) without any of its disjuncts being supertrue.