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Class 12MathematicsSetsEasyLevel 14

U = {1, 2, 3, ..., 120}; A is the set of numbers divisible by 3, B by 4, and C by 12. Which relation is correct?

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Answer and explanation

Correct answer: C = A ∩ B

A number is in A ∩ B exactly when it is divisible by both 3 and 4. Because lcm(3, 4) = 12, this condition is equivalent to being divisible by 12, which defines C. Thus C = A ∩ B. The union would include numbers divisible by only one of 3 or 4, while C is the smaller common set, so option A is the only correct relation.

Tags

setsintersectionset relationsLCMMathematicsClass 12 MCQ

Frequently asked questions

What is the correct answer to this question?

C = A ∩ B

Why is this the correct answer?

A number is in A ∩ B exactly when it is divisible by both 3 and 4. Because lcm(3, 4) = 12, this condition is equivalent to being divisible by 12, which defines C. Thus C = A ∩ B. The union would include numbers divisible by only one of 3 or 4, while C is the smaller common set, so option A is the only correct relation.

Which subject and chapter does this question cover?

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

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10 more MCQs
  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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