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 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)EasyLevel 17

If n(A) = 16, n(B) = 13, and n(A ∪ B) = 21, what is n(A ∩ B)?

Advertisement

Answer and explanation

Correct answer: 8

For two finite sets, the addition rule is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 21 = 16 + 13 − n(A ∩ B). Therefore n(A ∩ B) = 29 − 21 = 8. The subtraction is necessary because elements common to A and B are counted twice when n(A) and n(B) are added.

Tags

setscardinalityinclusion exclusionintersectionOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

8

Why is this the correct answer?

For two finite sets, the addition rule is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 21 = 16 + 13 − n(A ∩ B). Therefore n(A ∩ B) = 29 − 21 = 8. The subtraction is necessary because elements common to A and B are counted twice when n(A) and n(B) are added.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).

Report question
Advertisement