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When will the relation (R={(a,b):d(a,b)=2}) be symmetric, where (d) is a distance function?किस स्थिति में संबंध (R={(a,b):d(a,b)=2}) सममित होगा, जहाँ (d) दूरी फलन है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because distance satisfies (d(a,b)=d(b,a))क्योंकि दूरी में (d(a,b)=d(b,a)) होता है
Step 1: In a distance function, the distance between two points does not change when direction is reversed. Step 2: If (d(a,b)=2), then (d(b,a)=2) also holds. Step 3: Distance-based relations are usually symmetric because of this property.चरण 1: दूरी फलन में दो बिंदुओं की दूरी दिशा बदलने से नहीं बदलती। चरण 2: यदि (d(a,b)=2), तो (d(b,a)=2) भी होगा। चरण 3: दूरी आधारित संबंधों में सममितता सामान्यतः दूरी के इसी गुण से आती है।
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