If A ∪ B = {1, 2, 3, 4, 5, 6}, A ∩ B = {2, 5}, and A − B = {1, 4}, what is B − A?
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Answer and explanation
Correct answer: {3, 6}
The union is partitioned into three disjoint parts: A − B, A ∩ B, and B − A. The given parts account for {1, 4} and {2, 5}. Removing these four elements from A ∪ B = {1, 2, 3, 4, 5, 6} leaves {3, 6}. These remaining elements must be in B but not in A, so B − A = {3, 6}. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
{3, 6}
Why is this the correct answer?
The union is partitioned into three disjoint parts: A − B, A ∩ B, and B − A. The given parts account for {1, 4} and {2, 5}. Removing these four elements from A ∪ B = {1, 2, 3, 4, 5, 6} leaves {3, 6}. These remaining elements must be in B but not in A, so B − A = {3, 6}. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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