If W = {x ∈ Z : 1 ≤ x² < 25}, how many elements does W contain?
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Answer and explanation
Correct answer: 8
Because x is an integer and x² < 25, x must lie between −4 and 4 inclusive. Thus the possible values are −4, −3, −2, −1, 0, 1, 2, 3, and 4. The additional condition 1 ≤ x² excludes only x = 0, because 0² = 0. The remaining eight integers are −4, −3, −2, −1, 1, 2, 3, and 4. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Because x is an integer and x² < 25, x must lie between −4 and 4 inclusive. Thus the possible values are −4, −3, −2, −1, 0, 1, 2, 3, and 4. The additional condition 1 ≤ x² excludes only x = 0, because 0² = 0. The remaining eight integers are −4, −3, −2, −1, 1, 2, 3, and 4. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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