Class 11 Mathematics - Sets - Operations on Sets (Union, Intersection, Difference) Medium Quiz

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\(n(A-B)=16\) और \(n(A\cap B)=11\) है। (n\(A\)) कितना होगा?

\(n(A-B)=16\) and \(n(A\cap B)=11\). What is (n\(A\))?

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Correct Answer

A. 27

Explanation

Simple Explanation

सेट A को दो असांघि \(disjoint\) भागों में विभाजित किया जा सकता है: \(A-B\) और \(A\cap B\). इसलिए कार्डिनैलिटी जोड़नीय है: \(n(A)=n(A-B)+n(A\cap B)=16+11=27\). विकल्प C \(16\) केवल \(A-B\) के तत्व दिखाता है और विकल्प D \(11\) केवल सम्मिलन के तत्व — दोनों का योग ही पूर्ण A देता है। परीक्षा-सुझाव: किसी सेट के तत्व गिनते समय उसे असांघि उप-सेट्स में बाँटकर जोड़ें। / Set A splits into two disjoint parts: \(A-B\) and \(A\cap B\). Cardinalities of disjoint parts add, so \(n(A)=n(A-B)+n(A\cap B)=16+11=27\). Option C \(16\) counts only \(A-B\) and option D \(11\) counts only the intersection; neither alone gives the whole A. Exam tip: partition a set into disjoint pieces and add their cardinalities when counting elements.

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