$A / B$ set operation in boolean logic

Question

When doing $A / B$ set operation, is there an equavalency in boolean logic? For instance A union B is the equivalent to $A ∨ B$.

Answer 1

I think you mean A/B, where A/B={x|x∈A ∧ x∉B}. If that is what you mean, then I don't believe there is an exact Boolean correspondence. However, notice when we say A∪B={x|x∈A v x∈B}, there is a Boolean functor "or" in the set-builder notation of A∪B, and element-hood does not vary from set A to set B. On the other hand, looking back at A/B, we see that the definition of the set is dependent not only on the functor, but also on the concept of element-hood.

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Edit:

That said, Some have argue that there is a Boolean counterpart for set difference. That is, $(A \land \lnot B)$. However, it boils down to personal preference; or, perhaps if it there is any pragmatic value in treating it as such.

Also, for unions and intersections we can De Morgan distribute them like conjunction and disjunction; however, for difference we can do no such thing.