Final answer:
To prove the set identity A ∪ (B - A) = A ∪ B, we see that A ∪ (B - A) combines all elements of A with those in B not in A, while A ∪ B includes all elements of A and B. Since all elements of A are already in the union, the two sets are equivalent.
Step-by-step explanation:
To prove the set identity A ∪ (B - A) = A ∪ B, let's analyze what each part means and use set identities.
First, recall that B - A is the set of elements that are in B but not in A. When we take A ∪ (B - A), we are combining all elements in A with those elements in B that aren't already in A. However, since all elements of A are already included in the union by definition, adding (B - A) doesn't add any elements from A that weren't already there.
Now, let's look at A ∪ B. This union includes all elements that are in A, plus all elements that are in B, with no regard to whether the elements of B are in A or not. Therefore, the set A ∪ (B - A) will have all elements in A and all elements in B that are not in A. The set A ∪ B will have all the elements of A and all elements of B, which is effectively the same. Hence, we've shown that A ∪ (B - A) = A ∪ B.