Sets, Relations & Functions
Set Operations
Grade 11

Question:

<p>●13. A ∩ B equals</p>
<p>(a) [1, 7)</p>
<p>(b) [1, 3]</p>
<p>(c) (−7, 3]</p>
<p>(d) (−7, 1) ∪ (3, 7)</p>

Step-by-Step Solution

Key Concept: Find the solution sets for both inequalities separately, then find their intersection.
<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} = {x : 1 ≤ x ≤ 3} = [1, 3]</p><p>Therefore, A ∩ B = (−∞, ∞) ∩ [1, 3] = [1, 3]</p><p>∴ Answer is (b) [1, 3]</p>
Correct Answer: B

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