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If (R={(a,b):a,b\in\mathbb{R}\text{ and }0<a-b<2}), what type is (R)?यदि (R={(a,b):a,b\in\mathbb{R}\text{ और }0<a-b<2}), तो (R) कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Not transitiveसंक्रमण नहीं
Step 1: Take (a=3), (b=1.5), and (c=0). Step 2: (0<3-1.5<2) and (0<1.5-0<2), but (3-0=3), which is not less than (2). Step 3: In bounded inequalities, two small gaps can cross the bound.चरण 1: (a=3), (b=1.5), (c=0) लें। चरण 2: (0<3-1.5<2) और (0<1.5-0<2), पर (3-0=3), जो (2) से कम नहीं है। चरण 3: सीमा वाली असमानताओं में दो छोटी दूरियां मिलकर सीमा पार कर सकती हैं।
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