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Class 12MathematicsSetsEasyLevel 18
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If n(A − B) = 13 and n(A ∩ B) = 7, what is n(A)?

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Answer and explanation

Correct answer: 20

Set A can be partitioned into two disjoint parts: A − B, containing elements of A outside B, and A ∩ B, containing elements common to A and B. Therefore, n(A) = n(A − B) + n(A ∩ B). Substituting the given values gives n(A) = 13 + 7 = 20. Subtraction is not appropriate because the two given parts do not overlap. Thus, option B is correct.

Related tags

SetsCardinalitySet-DifferenceIntersectionMathematicsClass 12 Mcq

Frequently asked questions

What is the correct answer to this question?

20

Why is this the correct answer?

Set A can be partitioned into two disjoint parts: A − B, containing elements of A outside B, and A ∩ B, containing elements common to A and B. Therefore, n(A) = n(A − B) + n(A ∩ B). Substituting the given values gives n(A) = 13 + 7 = 20. Subtraction is not appropriate because the two given parts do not overlap. Thus, option B is correct.

Which subject and chapter does this question cover?

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

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  1. 1If Q = {x : x is a digit and x is prime}, which is the roster form of Q?
  2. 2Which is the roster form of F₁ = {x : x is a positive multiple of 3 or 5, and x < 20}?
  3. 3Which is the correct roster form of B = {x : x is a prime divisor of 84}?
  4. 4Which set best represents N = {2, 4, 8, 16, 32}?
  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}?
  7. 7If D₁ = {x : x ∈ ℤ, 2 < x² ≤ 16}, what is the roster form of D₁?
  8. 8The set E₁ = {x : x ∈ ℕ, x = 30/n, n ∈ ℕ} is equal to which set?
  9. 9Which option is the correct roster form of G₁ = {x : x ∈ ℤ, x³ = x}?
  10. 10What is the roster form of H₁ = {x : x ∈ ℕ, 5 ≤ x ≤ 15, x is composite}?
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