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Class 12MathematicsSetsMediumLevel 17
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If n(A \ B) = 17 and n(A ∩ B) = 11, what is n(A)?

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Answer and explanation

Correct answer: 28

Every element of A belongs to exactly one of two disjoint regions: A \ B, containing elements of A outside B, or A ∩ B, containing elements common to both sets. Therefore n(A) = n(A \ B) + n(A ∩ B) = 17 + 11 = 28. Options B and C count only one region, while option D does not represent the total. Hence option A is correct.

Related tags

SetsCardinalitySet-DifferenceIntersectionMathematicsClass 12 Mcq

Frequently asked questions

What is the correct answer to this question?

28

Why is this the correct answer?

Every element of A belongs to exactly one of two disjoint regions: A \ B, containing elements of A outside B, or A ∩ B, containing elements common to both sets. Therefore n(A) = n(A \ B) + n(A ∩ B) = 17 + 11 = 28. Options B and C count only one region, while option D does not represent the total. Hence option A is correct.

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Sets.

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  5. 5Which option is not an example of a well-defined set?
  6. 6What is the correct roster form of A₁ = {x : x ∈ ℕ, x² − 1 = 0}?
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  8. 8The set E₁ = {x : x ∈ ℕ, x = 30/n, n ∈ ℕ} is equal to which set?
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