If $x$ and $y$ are integer variables that have value $0$ or $1$, then what does the expression $x + y - xy$ mean?

You're right that "$-$" doesn't really have an interpretation as a binary operation of booleans, but, as the truth table shows, this whole expression does make sense even if it contains a component that does not. Subtraction does make sense in the unary operation that $1-x$ is "not $x$" in booleans.

Really, what is going on here is that we have the boolean identity: $$x\text{ or }y=\text{not }((\text{not } x)\text{ and }(\text{not }y))$$ and the right hand side encodes as $$1-(1-x)(1-y)$$ where all the subtractions have a clear interpretation. This just happens, in the world in integers, to be the same as $x+y-xy$ after distributing - even though this doesn't really make sense in the world of booleans.

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Logic

Discrete Mathematics

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