What does "x-y" denote in boolean logic?

Question

I came across this equation in set theory :

x-y = y'-x'
where x and y are sets

If it was a "+" or "." , I could easily correlate it with OR and AND function.
But what does this "-" indicate in boolean logic?
It indicates Set difference in set theory.
Is it complement ? But complement is denoted by " ' " here.

Answer 1

This says that $x$ and $y$ are sets. Denoting the complement of $z$ by $z'$, we have that $$x-y=x\cap y'$$ Intuitively, you are taking only the elements of $x$ that are not elements of $y$. This does not require $y$ to be a subset of $x$.

As you can work out, $$y'-x'=y'\cap (x')'=y'\cap x$$ so you can see the equivalence.

For the connection with Boolean logic, this is $x.y'$, or in the notation I am used to $x\wedge \neg y$.

Answer 2

Conclusion :
Set view : x - y = Elements in x but not in y
Focusing on terms "x", "BUT" which translates to "AND", "NOT" in y
Thus, Boolean view became x.y'

Other Set to Boolean views:
x ∩ y = Elements common to both = x.y
x ∪ y = Elements in both combined = x+y
x' = Elements not in x = x'
x Δ y = Elements in x or y but not in both = x ⊕ y = x.y' + x'.y

Uses of these boolean views over set views :
You don't need to go through the trouble of finding counter examples to prove any equation wrong. Just show it with boolean logic and put values for x,y as 0 or 1 and see it it satisfies.