  The idempotent law \(x^2 = x\) was different from Boole’s  laws for the common algebra—it only applied to the individual class symbols, not in general to compound terms that one could build from these symbols.  For example, one does not have  \((x + y)^2 = x + y\) in Boole’s system, otherwise   by ordinary algebra with idempotent class symbols, this would imply \(2xy = 0\), and then \(xy = 0\), which would force \(x\) and \(y\) to represent disjoint classes. But it is not the case that every pair of classes is disjoint. 