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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)MediumLevel 10

If |A ∪ B| = 70, |A \ B| = 25, and |B \ A| = 30, what is |A ∩ B|?

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Answer and explanation

Correct answer: 15

The union A ∪ B is divided into three pairwise disjoint regions: elements only in A, counted by |A \ B|; elements only in B, counted by |B \ A|; and common elements, counted by |A ∩ B|. Hence 70 = 25 + 30 + |A ∩ B|. Solving gives |A ∩ B| = 70 − 55 = 15, so option A is correct.

Tags

setscardinalityintersectionvenn-diagramdisjoint-regionsOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

15

Why is this the correct answer?

The union A ∪ B is divided into three pairwise disjoint regions: elements only in A, counted by |A \ B|; elements only in B, counted by |B \ A|; and common elements, counted by |A ∩ B|. Hence 70 = 25 + 30 + |A ∩ B|. Solving gives |A ∩ B| = 70 − 55 = 15, so 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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10 more MCQs
  1. 1If A = [1, 4] and B = (2, 5), what is A ∩ B?
  2. 2If A = (0, 3) and B = [3, 7], what is A ∩ B?
  3. 3If A = [−3, 2] and B = [0, 5], what is A ∪ B?
  4. 4If A = (1, 2) and B = (3, 4), how should A ∪ B be written?
  5. 5If A = (−∞, 4] and B = (1, ∞), what is A ∩ B?
  6. 6If A = {x ∈ R : x ≤ 0} and B = {x ∈ R : x ≥ 0}, what is A ∩ B?
  7. 7If A = (−4, 1] and B = [−2, 3), what is A \ B?
  8. 8If A = {x : x is a positive multiple of 2 or 3 less than 12}, what is A?
  9. 9If \(A=\{1,2,3,4\}\) and \(B=\{2,3\}\), which statement about \(A-B\) is correct?
  10. 10If A ⊆ B, which of the following statements is always true?
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