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If (A={1,2,3,4,5}), how many equivalence relations have (1,2,3) in the same class?यदि (A={1,2,3,4,5}) है, तो ऐसे समतुल्यता संबंधों की संख्या कितनी है जिनमें (1,2,3) एक ही वर्ग में हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (5)(5)
Step 1: Treat (1,2,3) as one combined block. Step 2: Now there are three units: ({1,2,3},4,5). Step 3: The number of partitions of three units is (5), so the answer is (5).चरण 1: (1,2,3) को एक संयुक्त समूह मान लें। चरण 2: अब तीन इकाइयां हैं: ({1,2,3},4,5)। चरण 3: तीन इकाइयों के विभाजन (5) होते हैं, इसलिए उत्तर (5) है।
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