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If A = {x : x ∈ Z, |x| < 3} and B = {-2, -1, 0, 1, 2}, which statement is correct?
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Answer and explanation
Correct answer: A = B
For integers, |x| < 3 is equivalent to -3 < x < 3. The integers strictly between -3 and 3 are -2, -1, 0, 1, and 2. Therefore A = {-2, -1, 0, 1, 2}, which is exactly B. Thus A = B. The number 3 is not in A because |3| = 3, which does not satisfy the strict inequality.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
For integers, |x| < 3 is equivalent to -3 < x < 3. The integers strictly between -3 and 3 are -2, -1, 0, 1, and 2. Therefore A = {-2, -1, 0, 1, 2}, which is exactly B. Thus A = B. The number 3 is not in A because |3| = 3, which does not satisfy the strict inequality.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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