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On (A={1,2,3,4,5}), (R) has classes ({1,2,3},{4,5}). Why is the complement of (R) not an equivalence relation?समुच्चय (A={1,2,3,4,5}) पर (R) के वर्ग ({1,2,3},{4,5}) हैं। (R) का पूरक तुल्यता संबंध क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because reflexivity failsक्योंकि स्वतुल्यता नहीं है
Step 1: Since (R) is an equivalence relation, every ((a,a)) is in (R). Step 2: Therefore no ((a,a)) remains in the complement. Step 3: Without reflexivity, the complement cannot be an equivalence relation.चरण 1: (R) एक तुल्यता संबंध है, इसलिए हर ((a,a)) उसमें है। चरण 2: पूरक में कोई भी ((a,a)) नहीं बचेगा। चरण 3: स्वतुल्यता न होने से पूरक तुल्यता संबंध नहीं हो सकता।
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