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For a relation (R) on set (A), which condition is equivalent to reflexivity?समुच्चय (A) पर संबंध (R) के लिए कौन-सी शर्त स्ववाचीता के तुल्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\Delta_A \subseteq R)(\Delta_A \subseteq R)
Step 1: (\Delta_A) contains all diagonal pairs ((a,a)). Step 2: (R) is reflexive exactly when all these diagonal pairs are included in (R). Step 3: Therefore (\Delta_A \subseteq R) is the concise equivalent condition for reflexivity.चरण 1: (\Delta_A) में सभी ((a,a)) विकर्ण युग्म होते हैं। चरण 2: (R) स्ववाची तभी है जब ये सभी विकर्ण युग्म (R) में शामिल हों। चरण 3: इसलिए (\Delta_A \subseteq R) स्ववाचीता की छोटी और सटीक शर्त है।
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