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If A = {x ∈ R : x² < 9} and B = {x ∈ R : x ≥ 1}, what is A ∩ B?
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Answer and explanation
Correct answer: [1, 3)
The inequality x² < 9 means −3 < x < 3, so A = (−3, 3). Set B contains all real numbers x ≥ 1, so B = [1, ∞). The intersection must satisfy both conditions simultaneously: x must be at least 1 and less than 3. Thus 1 is included and 3 is excluded, giving A ∩ B = [1, 3).
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What is the correct answer to this question?
[1, 3)
Why is this the correct answer?
The inequality x² < 9 means −3 < x < 3, so A = (−3, 3). Set B contains all real numbers x ≥ 1, so B = [1, ∞). The intersection must satisfy both conditions simultaneously: x must be at least 1 and less than 3. Thus 1 is included and 3 is excluded, giving A ∩ B = [1, 3).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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