We are given two sets A and B, and we need to find what (A−B) ∪ (B−A) equals. Let's break this down step by step.

The set difference A−B (also written as A \ B) contains all elements that are in A but not in B.

Mathematically: $A - B = {x ∣ x \in A and x \notin B}$

Similarly, B−A contains all elements that are in B but not in A.

Mathematically: $B - A = {x ∣ x \in B and x \notin A}$

The union (A−B) ∪ (B−A) combines all elements that are exclusively in A or exclusively in B. It excludes any elements that are in both A and B.

This combined set is known as the Symmetric Difference of A and B, often denoted by A Δ B.

Imagine a Venn diagram with two overlapping circles for sets A and B.

A−B is the part of circle A that does not overlap with circle B.
B−A is the part of circle B that does not overlap with circle A.
Their union is the entire area of the two circles, excluding the overlapping center region (A∩B).

This visually represents the set (A∪B) − (A∩B).

Let's evaluate each option:

A∪B: This includes all elements in A or B or both. This is larger than our set because it includes the intersection A∩B, which we specifically excluded.
(A∩B) − (A∪B): The set difference (A∩B) − (A∪B) is always an empty set (∅) because A∩B is a subset of A∪B. Subtracting a superset from its subset leaves nothing. This is not our set.
(A∪B) − (A∩B): This is exactly the set of all elements that are in A or B but not in both. This matches our definition of the symmetric difference perfectly.
A∩B: This is only the elements common to both sets. Our set explicitly excludes these, so this is the opposite of our set.

Therefore, (A−B) ∪ (B−A) equals (A∪B) − (A∩B).

Set Theory: The branch of mathematics that deals with sets, or collections of objects.
Set Operations: Fundamental operations like union (∪), intersection (∩), difference (−), and complement.
Symmetric Difference: An important operation that gives the set of elements which are in either of the sets but not in their intersection.
Venn Diagrams: Visual diagrams used to represent sets and their relationships.

Note: The two definitions for symmetric difference are equivalent, as proven in the solution above.