 Boole’s three laws for his algebra of logic are woefully inadequate for what follows in MAL. The reader will, for the most part, be well served by assuming that Boole is doing ordinary polynomial algebra augmented by the assumption that any power \(x^n\) of an elective symbol \(x\) can be replaced by \(x\).  One can safely assume that any polynomial equation p = q that holds  in Common Algebra is valid in Boole’s algebra as is any equational argument