Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 12MathematicsSetsHardLevel 15
0 reads0 ratings0 helpful

If n(A ∪ B ∪ C) = 95, exactly one set contains 46 elements, and exactly two sets contain 33 elements, what is n(A ∩ B ∩ C)?

Advertisement

Answer and explanation

Correct answer: 16

The union of three sets is divided into three mutually exclusive categories: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Hence 95 = 46 + 33 + n(A ∩ B ∩ C). Solving gives n(A ∩ B ∩ C) = 95 − 79 = 16. The categories must be added once each because they do not overlap.

Related tags

SetsVenn DiagramsTriple IntersectionThree-Set CountingMathematicsClass 12 Mcq

Frequently asked questions

What is the correct answer to this question?

16

Why is this the correct answer?

The union of three sets is divided into three mutually exclusive categories: elements in exactly one set, elements in exactly two sets, and elements in all three sets. Hence 95 = 46 + 33 + n(A ∩ B ∩ C). Solving gives n(A ∩ B ∩ C) = 95 − 79 = 16. The categories must be added once each because they do not overlap.

Which subject and chapter does this question cover?

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

Was this question useful?

No ratings yetWrite a review / Rate this question

Student Reviews

No published reviews yet.

KEEP PRACTISING

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}?
Advertisement