Step-by-Step Solution
Key Concept: The set difference (A ∪ B) - (A ∩ B) represents elements that belong to at least one set but not to both simultaneously. This is precisely the symmetric difference, which equals (A - B) ∪ (B - A).
<p><strong>Step 1:</strong> Understand what (A ∪ B) - (A ∩ B) means: elements in the union but not in the intersection.</p><p><strong>Step 2:</strong> Break down elements:</p><ul><li>A ∪ B contains: elements only in A, only in B, and in both A and B</li><li>A ∩ B contains: elements in both A and B</li></ul><p><strong>Step 3:</strong> After removing A ∩ B from A ∪ B, we're left with elements that are in A but not B, plus elements in B but not A.</p><p><strong>Step 4:</strong> This equals (A - B) ∪ (B - A), which is the symmetric difference A △ B.</p><p><strong>Verification:</strong> For any element x:<br>x ∈ (A ∪ B) - (A ∩ B) ⟺ (x ∈ A or x ∈ B) and not (x ∈ A and x ∈ B)<br>⟺ (x ∈ A and x ∉ B) or (x ∈ B and x ∉ A)<br>⟺ x ∈ (A - B) ∪ (B - A)</p><p>∴ Answer: <strong>C: (A - B) ∪ (B - A) or A △ B</strong></p>
Correct Answer: C