If F = {x : x ∈ ℤ, |x + 1| ≤ 2}, what is the number of elements in F?
Answer and explanation
Correct answer: 5
The condition |x + 1| ≤ 2 means that x + 1 lies between −2 and 2, inclusive. Therefore, −2 ≤ x + 1 ≤ 2. Subtracting 1 from all three parts gives −3 ≤ x ≤ 1. Since x must be an integer, the possible values are −3, −2, −1, 0, and 1. There are 5 values, so the set F has 5 elements. The endpoints are included because the inequality is ‘less than or equal to’.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The condition |x + 1| ≤ 2 means that x + 1 lies between −2 and 2, inclusive. Therefore, −2 ≤ x + 1 ≤ 2. Subtracting 1 from all three parts gives −3 ≤ x ≤ 1. Since x must be an integer, the possible values are −3, −2, −1, 0, and 1. There are 5 values, so the set F has 5 elements. The endpoints are included because the inequality is ‘less than or equal to’.
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.
