  Boole used lower case Latin letters at the end of the alphabet, like \(x,y,z\), to represent classes. The universe was a class, denoted by 1; and there was a class described as “Nothing”,  denoted by 0, which we call the empty class. The operation of multiplication was defined to be what we call intersection, and this led to his first law, \(xy = yx\), and then to the idempotent law \(x^2 = x\). Addition was introduced as aggregation when the classes were disjoint. He stated the commutative law for addition, \(x + y = y + x\), and the distributive law \(z(x + y) = zx + zy\). Then followed \(x - y = - y + x\) and \(z(x - y) = zx - zy\). The associative laws for addition and multiplication were conspicuously absent. 