Which option gives the correct roster form of Q = {x : x ∈ W and x² < 10}, where W = {0, 1, 2, ...}?
Answer and explanation
Correct answer: Q = {0, 1, 2, 3}
Use the defining condition x² < 10 and remember that W contains only non-negative integers. We have 0² = 0, 1² = 1, 2² = 4 and 3² = 9, all less than 10. But 4² = 16, so 4 is excluded. Negative numbers cannot be included because they are not whole numbers. Hence the roster form is Q = {0, 1, 2, 3}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Q = {0, 1, 2, 3}
Why is this the correct answer?
Use the defining condition x² < 10 and remember that W contains only non-negative integers. We have 0² = 0, 1² = 1, 2² = 4 and 3² = 9, all less than 10. But 4² = 16, so 4 is excluded. Negative numbers cannot be included because they are not whole numbers. Hence the roster form is Q = {0, 1, 2, 3}, so option A is correct.
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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