How many elements are there in T = {x : x ∈ Z, x² ≤ 4}?
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Answer and explanation
Correct answer: 5
Since x² ≤ 4, taking square roots gives −2 ≤ x ≤ 2. The set is restricted to integers, so the possible values are −2, −1, 0, 1, and 2. These are five distinct elements. The endpoints are included because the inequality is less than or equal to 4. Hence the cardinality of T is 5, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Since x² ≤ 4, taking square roots gives −2 ≤ x ≤ 2. The set is restricted to integers, so the possible values are −2, −1, 0, 1, and 2. These are five distinct elements. The endpoints are included because the inequality is less than or equal to 4. Hence the cardinality of T is 5, so option C 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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