If A = {x ∈ R : |x − 2| ≤ 3} and B = {x ∈ R : x² ≤ 4}, what is A ∩ B?
Answer and explanation
Correct answer: [-1,2]
Solve the first inequality by removing the absolute value: |x − 2| ≤ 3 means −3 ≤ x − 2 ≤ 3. Adding 2 throughout gives −1 ≤ x ≤ 5, so A = [-1,5]. The second inequality x² ≤ 4 means −2 ≤ x ≤ 2, so B = [-2,2]. The common part of these two closed intervals starts at -1 and ends at 2. Therefore, A ∩ B = [-1,2].
Frequently asked questions
What is the correct answer to this question?
[-1,2]
Why is this the correct answer?
Solve the first inequality by removing the absolute value: |x − 2| ≤ 3 means −3 ≤ x − 2 ≤ 3. Adding 2 throughout gives −1 ≤ x ≤ 5, so A = [-1,5]. The second inequality x² ≤ 4 means −2 ≤ x ≤ 2, so B = [-2,2]. The common part of these two closed intervals starts at -1 and ends at 2. Therefore, A ∩ B = [-1,2].
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
