Zero is even as is well established. It is both an integer and a multiple of 2. The whole number system is unfair. It is particularly unfair when applied to money.
What can we say about** the set of functions F such that F(a) + F(b) = F(ab) ?
[[ Perhaps simpler is the set G such that G(a) + G(b) = G(a+b) because G(x) = k*x is one such function (linear). If G is the unitary function such that G(x) = x, then the relation is trivially always true. ]]
If F is the unitary function such that F(x) = x, then this imposes the symmetric condition on a,b: a = b / (b-1) and (a-1)*(b-1) = 1.
Anyway: do any F's exist which are true for all a,b? and if so, what are they? How the hell do you even begin to solve this?
** "Goes nicely with a piece of toast" is not acceptable
In Boolean logic OR can be represented "+" and AND represented "×". NOT is the "-" operator. Then syllogisms work if TRUE=1 and FALSE = 0. As you know well. So over the field of Boolean algebra (i.e 0 and 1) the proposition holds.