If A = {x ∈ ℤ : x² ≤ 9}, how many elements are in A?
Answer and explanation
Correct answer: 7
For an integer x, the inequality x² ≤ 9 means −3 ≤ x ≤ 3. The integers in this closed interval are −3, −2, −1, 0, 1, 2, and 3. Counting them gives 7 elements. The endpoints must be included because the inequality is ‘less than or equal to,’ not strictly less than. Therefore, the cardinality of A is 7.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For an integer x, the inequality x² ≤ 9 means −3 ≤ x ≤ 3. The integers in this closed interval are −3, −2, −1, 0, 1, 2, and 3. Counting them gives 7 elements. The endpoints must be included because the inequality is ‘less than or equal to,’ not strictly less than. Therefore, the cardinality of A is 7.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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