<p>●15. A ∪ B equals</p>
Step-by-Step Solution
Key Concept: Since A is the entire real number line, the union of A with any set B is simply A.
<p><strong>Solution:</strong></p><p>Given: A = {x : x² − 2x + 2 > 0} = {x : (x − 1)² + 1 > 0} = (−∞, ∞)</p><p>B = {x : x² − 4x + 3 ≤ 0} = {x : (x − 1)(x − 3) ≤ 0} = [1, 3]</p><p>A ∪ B = (−∞, ∞) ∪ [1, 3] = (−∞, ∞)</p><p>∴ Answer is (c) (−∞, ∞)</p>
Correct Answer: C