If A = {x ∈ R : x² ≤ 16} and B = {x ∈ R : x > 1}, what is the interval form of A ∩ B?
Answer and explanation
Correct answer: (1, 4]
The inequality x² ≤ 16 is equivalent to −4 ≤ x ≤ 4, so A = [−4, 4]. Set B contains numbers strictly greater than 1. To belong to the intersection, a number must satisfy both conditions, giving 1 < x ≤ 4. The lower endpoint 1 is excluded and the upper endpoint 4 is included, so A ∩ B = (1, 4]. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
(1, 4]
Why is this the correct answer?
The inequality x² ≤ 16 is equivalent to −4 ≤ x ≤ 4, so A = [−4, 4]. Set B contains numbers strictly greater than 1. To belong to the intersection, a number must satisfy both conditions, giving 1 < x ≤ 4. The lower endpoint 1 is excluded and the upper endpoint 4 is included, so A ∩ B = (1, 4]. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
