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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 17

If A △ B = (A \ B) ∪ (B \ A), |A| = 21, |B| = 19, and |A ∩ B| = 8, what is |A △ B|?

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Answer and explanation

Correct answer: 24

The symmetric difference contains elements that belong to exactly one of A and B, so the common elements must be excluded from both sets. Its cardinality is |A △ B| = |A| + |B| − 2|A ∩ B|. Substituting the given values gives 21 + 19 − 2(8) = 40 − 16 = 24. Therefore, option A is correct.

Tags

setssymmetric differencecardinalityintersectionset operationsOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

24

Why is this the correct answer?

The symmetric difference contains elements that belong to exactly one of A and B, so the common elements must be excluded from both sets. Its cardinality is |A △ B| = |A| + |B| − 2|A ∩ B|. Substituting the given values gives 21 + 19 − 2(8) = 40 − 16 = 24. Therefore, 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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