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If (R) is not transitive, will (R\cup\Delta) always become transitive?यदि (R) संक्रमण नहीं है, तो (R\cup\Delta) हमेशा संक्रमण हो जाएगा या नहीं?
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Correct answer:सही उत्तर: Noनहीं
Step 1: Identity pairs only fill self-pair gaps like ((a,a)). Step 2: If the missing pair is like ((1,3)), (\Delta) will not add it. For example, ({(1,2),(2,3)}) still lacks ((1,3)). Step 3: Not every missing pair is a self-pair.चरण 1: पहचान जोड़ियां केवल ((a,a)) जैसी कमी भरती हैं। चरण 2: यदि गुम जोड़ी ((1,3)) जैसी हो, तो (\Delta) उसे नहीं जोड़ेगा। जैसे ({(1,2),(2,3)}) में ((1,3)) अब भी नहीं आएगा। चरण 3: हर कमी समान तत्व वाली नहीं होती।
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