How many elements are in the set {x ∈ ℤ : x² < 10}?
Answer and explanation
Correct answer: 7
For x² < 10, we need −√10 < x < √10. Since √10 is approximately 3.16 and x must be an integer, the permitted values are −3, −2, −1, 0, 1, 2, and 3. There are seven distinct integers in this set. The set is finite because its elements are bounded between −√10 and √10. Therefore, its cardinality is 7, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For x² < 10, we need −√10 < x < √10. Since √10 is approximately 3.16 and x must be an integer, the permitted values are −3, −2, −1, 0, 1, 2, and 3. There are seven distinct integers in this set. The set is finite because its elements are bounded between −√10 and √10. Therefore, its cardinality is 7, so option C is correct.
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.
