Okay you are right, fair enough. But his equations are consistent with working over F2 (where we can then throw in additional simplifications) and treating mult

Okay you are right, fair enough. But his equations are consistent with working over F2 (where we can then throw in additional simplifications) and treating multiplication as AND and addition as XOR, in a way that using an algebra of ∧ and ∨ is not. When Boole writes "x xor y" as x(1 − y) + (1 − x)y = 1 ⟺ x − 2xy + y = 1 (p. 53, eq. 31), we can simplify by 2 = 0 and write x + y = 1, treating + here to mean exclusive or.