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On (A={1,2,3,4,5,6}), how many equivalence relations have class sizes (2,2,2)?समुच्चय (A={1,2,3,4,5,6}) पर ऐसे समतुल्यता संबंधों की संख्या कितनी है जिनके वर्गों के आकार (2,2,2) हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (15)(15)
Step 1: We must split six elements into three two-element classes. Step 2: The count is (\frac{6!}{(2!)^3\cdot3!}). Step 3: This equals (15), so there are (15) such equivalence relations.चरण 1: छह अवयवों को तीन दो-अवयवी वर्गों में बांटना है। चरण 2: गिनती (\frac{6!}{(2!)^3\cdot3!}) होगी। चरण 3: इसका मान (15) है, इसलिए इतने समतुल्यता संबंध बनेंगे।
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