If A = {x ∈ ℤ : x² − 9 < 0}, how many elements does A have?
Answer and explanation
Correct answer: 5
The governing concept is determining the cardinality of a set defined by an integer inequality. Starting with x² − 9 < 0 gives x² < 9, which is equivalent to −3 < x < 3. Since x must be an integer, the allowed values are −2, −1, 0, 1, and 2. There are 5 elements. The endpoints −3 and 3 are excluded because the inequality is strict, so options B, C, and D overcount or undercount the set.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The governing concept is determining the cardinality of a set defined by an integer inequality. Starting with x² − 9 < 0 gives x² < 9, which is equivalent to −3 < x < 3. Since x must be an integer, the allowed values are −2, −1, 0, 1, and 2. There are 5 elements. The endpoints −3 and 3 are excluded because the inequality is strict, so options B, C, and D overcount or undercount the set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
