If A = (-∞, 2] and B = (0, ∞), then what is (A ∩ B) ∪ (A \ B)?
Answer and explanation
Correct answer: A = (-∞, 2]
The set A is divided into two disjoint parts: A ∩ B, containing elements of A that are also in B, and A \ B, containing elements of A that are not in B. Every element of A belongs to exactly one of these parts. Therefore, their union reconstructs the entire set A. Here A ∩ B = (0, 2] and A \ B = (-∞, 0], whose union is (-∞, 2] = A.
Frequently asked questions
What is the correct answer to this question?
A = (-∞, 2]
Why is this the correct answer?
The set A is divided into two disjoint parts: A ∩ B, containing elements of A that are also in B, and A \ B, containing elements of A that are not in B. Every element of A belongs to exactly one of these parts. Therefore, their union reconstructs the entire set A. Here A ∩ B = (0, 2] and A \ B = (-∞, 0], whose union is (-∞, 2] = A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
