Proof:

Claim: (A ∪ B) - A = B - A

Explanation:

1. Definition:
- The set (A ∪ B) represents all elements that are in set A or set B or both.
- The operation A - B represents all elements that are in set A but not in set B.

2. (A ∪ B) - A:
- (A ∪ B) - A represents all elements that are in the union of sets A and B but not in set A.
- This means we are considering all elements that are only in B or in the intersection of A and B.

3. B - A:
- B - A represents all elements that are in set B but not in set A.
- This set includes elements that are in B but not in the intersection of A and B.

4. Proving the Claim:
- To prove that (A ∪ B) - A = B - A, we need to show that both sets contain the same elements.
- Since the elements in (A ∪ B) - A are in B but not in A, they are exactly the elements in B - A.
- Therefore, (A ∪ B) - A = B - A.

Conclusion:
- By using the property of sets and understanding the definitions of set operations, we have proved that (A ∪ B) - A is equal to B - A. This equality holds true for any sets A and B.