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On (A={-3,-2,-1,0,1,2,3}), (R={(a,b):ab\leq a^2}). Is (R) reflexive?समुच्चय (A={-3,-2,-1,0,1,2,3}) पर (R={(a,b):ab\leq a^2}) है। (R) प्रतिवर्ती है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Yesहाँ
Step 1: For reflexivity, put (b=a). Step 2: Then (ab=a^2), so the condition becomes (a^2\leq a^2), which is true. Step 3: Equality is included in (\leq), so every diagonal pair works.चरण 1: प्रतिवर्तिता के लिए (b=a) रखें। चरण 2: तब (ab=a^2) होगा, इसलिए शर्त (a^2\leq a^2) बनती है, जो सत्य है। चरण 3: बराबरी वाली स्थिति भी (\leq) में शामिल होती है।
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