Using (A \ B) ∪ (A ∩ B) = A, how are these two parts of A related?
Answer and explanation
Correct answer: They are disjoint.
The set A \ B contains elements of A that are outside B, whereas A ∩ B contains elements of A that are inside B. An element cannot simultaneously be outside B and inside B. Therefore (A \ B) ∩ (A ∩ B) = ∅, so the two parts are disjoint. Their union is A because every element of A is either in B or not in B.
Frequently asked questions
What is the correct answer to this question?
They are disjoint.
Why is this the correct answer?
The set A \ B contains elements of A that are outside B, whereas A ∩ B contains elements of A that are inside B. An element cannot simultaneously be outside B and inside B. Therefore (A \ B) ∩ (A ∩ B) = ∅, so the two parts are disjoint. Their union is A because every element of A is either in B or not in B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
