If V = {x : x ∈ Z and |x| < 3}, what is V?
Answer and explanation
Correct answer: V = {-2, -1, 0, 1, 2}
For an integer x, the condition |x| < 3 means that x is fewer than three units from zero. It is equivalent to −3 < x < 3. The integers strictly between these endpoints are −2, −1, 0, 1 and 2, so V = {−2, −1, 0, 1, 2}. The endpoints −3 and 3 are excluded because the inequality is strict, and zero is included because |0| = 0.
Frequently asked questions
What is the correct answer to this question?
V = {-2, -1, 0, 1, 2}
Why is this the correct answer?
For an integer x, the condition |x| < 3 means that x is fewer than three units from zero. It is equivalent to −3 < x < 3. The integers strictly between these endpoints are −2, −1, 0, 1 and 2, so V = {−2, −1, 0, 1, 2}. The endpoints −3 and 3 are excluded because the inequality is strict, and zero is included because |0| = 0.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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