If A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find (A – B) ⋃ (B – A).

Analyze the question: We need the symmetric difference of A and B. This means the elements that are in A only or in B only, but not in both.

Concept:

• A – B = elements in A that are not in B
• B – A = elements in B that are not in A
• ⋃ (union) = combine all elements from both sets

Solution:

1. A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}
2. Common elements (A ∩ B) = {2, 4, 6}
3. A – B: remove 2, 4, 6 from A, giving {1, 3, 5}
4. B – A: remove 2, 4, 6 from B, giving {8}
5. (A – B) ⋃ (B – A) = {1, 3, 5} ⋃ {8} = {1, 3, 5, 8}

Answer: Option A, {1, 3, 5, 8}.

Tip: (A – B) ⋃ (B – A) is the symmetric difference. It equals (A ⋃ B) – (A ∩ B). Here, A ⋃ B = {1, 2, 3, 4, 5, 6, 8}, and removing the common elements {2, 4, 6} leaves {1, 3, 5, 8}. This is a quick way to check your answer.