If A and B are two overlapping sets, what is A − (A ∩ B) equal to?
Answer and explanation
Correct answer: A − B
The set A ∩ B contains precisely those elements common to A and B. Subtracting this common part from A leaves the elements that are in A but not in B. By definition, that remainder is A − B. Algebraically, A − (A ∩ B) = A ∩ (A ∩ B)ᶜ = A ∩ Bᶜ = A − B. Thus option A is the only correct answer; the intersection is the part removed, not the part retained.
Frequently asked questions
What is the correct answer to this question?
A − B
Why is this the correct answer?
The set A ∩ B contains precisely those elements common to A and B. Subtracting this common part from A leaves the elements that are in A but not in B. By definition, that remainder is A − B. Algebraically, A − (A ∩ B) = A ∩ (A ∩ B)ᶜ = A ∩ Bᶜ = A − B. Thus option A is the only correct answer; the intersection is the part removed, not the part retained.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
