If A = {x ∈ R : x ≤ 1} and B = {x ∈ R : x > −2}, what is A ∩ B?
Answer and explanation
Correct answer: (−2, 1]
An intersection contains only numbers satisfying both conditions. The condition from A is x ≤ 1, and the condition from B is x > −2. Combining them gives −2 < x ≤ 1. In interval notation this is (−2, 1]. The left endpoint is open because −2 is excluded, while the right endpoint is closed because 1 is included.
Frequently asked questions
What is the correct answer to this question?
(−2, 1]
Why is this the correct answer?
An intersection contains only numbers satisfying both conditions. The condition from A is x ≤ 1, and the condition from B is x > −2. Combining them gives −2 < x ≤ 1. In interval notation this is (−2, 1]. The left endpoint is open because −2 is excluded, while the right endpoint is closed because 1 is included.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
