This is the obvious solution I was looking for. Thanks! (and I rightfully feel stupid now)

The formula is slightly wrong though. This is the right one:

a or b = a + b - (a * b)

The last term is equivalent to a conjunction. Which also makes sense when you think of probability:

P(a or b) = P(a) + P(b) - P(a and b)

Awesome, thanks!

I've seen this formula I think, and for mod 2 addition, there is no difference I guess.

True, but in modulo 2, + and - are the same. I chose the + to keep the formula simple.