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 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 20

If n(U) = 90, n(Aᶜ) = 35, n(Bᶜ) = 50, and n(Aᶜ ∩ Bᶜ) = 18, what is n(A ∩ B)?

Advertisement

Answer and explanation

Correct answer: 23

First find the cardinality of Aᶜ ∪ Bᶜ using the inclusion–exclusion formula: n(Aᶜ ∪ Bᶜ) = n(Aᶜ) + n(Bᶜ) − n(Aᶜ ∩ Bᶜ) = 35 + 50 − 18 = 67. By De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. Therefore, n((A ∩ B)ᶜ) = 67. Since the universal set has 90 elements, n(A ∩ B) = 90 − 67 = 23. Hence, option A is correct.

Tags

setscomplementde_morgancardinalityintersectionMathematicsComplement of a Set and Its PropertiesClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

23

Why is this the correct answer?

First find the cardinality of Aᶜ ∪ Bᶜ using the inclusion–exclusion formula: n(Aᶜ ∪ Bᶜ) = n(Aᶜ) + n(Bᶜ) − n(Aᶜ ∩ Bᶜ) = 35 + 50 − 18 = 67. By De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. Therefore, n((A ∩ B)ᶜ) = 67. Since the universal set has 90 elements, n(A ∩ B) = 90 − 67 = 23. Hence, option A is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.

Report question
Advertisement