If A = {x ∈ R : x ≤ 0} and B = {x ∈ R : x > 2}, what is A ∩ B?
Answer and explanation
Correct answer: ∅
For a real number to belong to A ∩ B, it must satisfy both conditions simultaneously: x ≤ 0 and x > 2. These conditions are incompatible, because every number greater than 2 is also greater than 0 and therefore cannot be at most 0. No real number satisfies both conditions, so the intersection is the empty set ∅.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
For a real number to belong to A ∩ B, it must satisfy both conditions simultaneously: x ≤ 0 and x > 2. These conditions are incompatible, because every number greater than 2 is also greater than 0 and therefore cannot be at most 0. No real number satisfies both conditions, so the intersection is the empty set ∅.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
