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If (R={(a,b):a,b\in\mathbb{R}\text{ and }|a-b|<1}), is (R) transitive?यदि (R={(a,b):a,b\in\mathbb{R}\text{ और }|a-b|<1}), तो क्या (R) संक्रमण है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Noनहीं
Step 1: Take (a=0), (b=0.6), and (c=1.2). Step 2: (|0-0.6|<1) and (|0.6-1.2|<1), but (|0-1.2|<1) is false. Step 3: In distance-based relations, two small distances may combine into a larger one.चरण 1: (a=0), (b=0.6), (c=1.2) लें। चरण 2: (|0-0.6|<1) और (|0.6-1.2|<1), पर (|0-1.2|<1) नहीं है। चरण 3: दूरी आधारित संबंधों में दो छोटी दूरियां मिलकर बड़ी दूरी बना सकती हैं।
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