 Boole analyzed the seven hypothetical syllogisms that were standard in Aristotelian logic, from the Constructive and Destructive Conditionals to the Complex Destructive Dilemma. Letting capital letters \(X, Y, \ldots\) represent categorical propositions, the hypothetical propositions traditionally involved in hypothetical syllogisms were in one of the forms \(X\) is true, \(X\) is false, If \(X\) is true then \(Y\) is true, \(X\) is true or \(Y\) is true or  …,  as well as  \(X\) is true and \(Y\) is true and …   At the end of the chapter on hypothetical syllogisms he noted that it was easy to create new ones, and one could enrich the collection by using mixed hypothetical propositions such as If \(X\) is true, then either \(Y\) is true, or \(Z\) is true. 