If A ⊆ U, B ⊆ U, and A − B = A ∩ B′, then (A − B) ∪ (A ∩ B) is equal to which of the following?
Answer and explanation
Correct answer: A
Every element of A falls into exactly one of two cases: it is either outside B, in which case it belongs to A − B, or it is inside B, in which case it belongs to A ∩ B. These two parts are disjoint and together contain all elements of A. Hence (A − B) ∪ (A ∩ B) = A. The expression cannot generally equal B or A ∪ B because those may contain elements outside A.
Frequently asked questions
What is the correct answer to this question?
A
Why is this the correct answer?
Every element of A falls into exactly one of two cases: it is either outside B, in which case it belongs to A − B, or it is inside B, in which case it belongs to A ∩ B. These two parts are disjoint and together contain all elements of A. Hence (A − B) ∪ (A ∩ B) = A. The expression cannot generally equal B or A ∪ B because those may contain elements outside 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).
