Why are set operations always showed with a Venn Diagram where both A and B are intersecting?

Question

So there is this question involving the pictorial representations of set operations (i.e. $A - B$).

In each Venn Diagram, the A and B circles (sets) are always shown overlapping. For example, $A - B$:

$A - B$">

What if the circles $A$ and $B$ were separate? How would defining the set operation be showed? Thanks.

Answer 1

In Venn diagrams, the circles are shown to intersect each other to provide for all possible scenarios. Now dots (representing elements) that lie in both circles in such diagrams represent elements that belong to both sets, and if these two sets are disjoint (have no elements in common), that just means that there are really no dots lying in both circles. If the circles were drawn as non-intersecting, there would be no way to represent elements that belong to both sets.

Answer 2

I am assuming that you are using $A-B$ to denote $A\setminus B$, and that the right-hand circle is $A$, while the other is $B$. If the circles were not overlapping, then $A\cap B=\emptyset$. In that case:$$A-B=A\setminus B=A$$