 Suppose all three operations are accepted (in which case all the Bs are true). It is then possible to define an operation in terms of negation and conjunction which behaves almost exactly like disjunction. Let \(\varrho(F)\) be the set of all sets of facts \(G\) with \(G \ne \varnothing\) and \(\DES(G) \ne W\). Where \(H\) is any set of facts, we let \(\mathbf{n}H\) be \(\{x^\textbf{n}\) : \(x\in H\cap F^{\#}\}\), the negative image of \(H\). This disjunction-like operation, \(\cdot^{\delta}\), is a (total) function from \(\varrho(F)\) to \(F^{\#}\) defined by the following condition: \(G^{\delta} = (\mathbf{n}G)^{\textbf{{cn}}}\). \(\cdot^{\delta}\) behaves like disjunction in that it satisfies the principles resulting from replacing ‘\(P(F)^*\)’ by ‘\(\varrho(F)\)’ in D1–D4.