 Most important in this chapter was Boole’s  claim that his algebra of logic for categorical propositions was equally suited to the study of hypothetical syllogisms. This was based on adopting the standard reduction of hypothetical propositions to propositions about classes by letting the hypothetical universe, also denoted by 1,  “comprehend all conceivable cases and conjunctures of circumstances”. Evidently his notion of a case  was an assignment of truth values to the propositional variables. For \(X\) a categorical proposition Boole let \(x\) denote the elective operator that selects the cases for which \(X\) is true.  