  By not viewing propositional formulas as functions on \(\{\)T, F\(\}\) Boole missed out on being the inventor of truth tables. His algebraic method of analyzing hypothetical syllogisms was to transform each of the hypothetical premises into an elective equation, and then apply his algebra of logic (which was developed for categorical propositions). For example, the premises \(X\) is true or \(Y\) is true, with or inclusive, and \(X\) is false  are expressed by the equations \(x + y - xy = 1\) and \(x = 0\). From these it immediately follows that \(y = 1\), giving the conclusion \(Y\) is true. 