If A = {3, 6, 9, 12} and B = {6, 12, 18, 24}, what is (A − B) ∩ (B − A)?
Answer and explanation
Correct answer: ∅
Compute both directed differences. A − B contains elements in A but not B, so A − B = {3, 9}. Likewise, B − A contains elements in B but not A, giving B − A = {18, 24}. These two sets are disjoint, meaning they have no common element. Their intersection is therefore the empty set, ∅, so option C is correct. Option D is only the first difference and is not the final intersection.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
Compute both directed differences. A − B contains elements in A but not B, so A − B = {3, 9}. Likewise, B − A contains elements in B but not A, giving B − A = {18, 24}. These two sets are disjoint, meaning they have no common element. Their intersection is therefore the empty set, ∅, so option C is correct. Option D is only the first difference and is not the final intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
