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On integers, the relation (R={(a,b):a-b=3}) is given. Why is it not symmetric?पूर्णांकों पर संबंध (R={(a,b):a-b=3}) दिया है। यह सममित क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (4-1=3), but (1-4\ne3)क्योंकि (4-1=3), लेकिन (1-4\ne3)
Step 1: To test symmetry, check one pair and its reverse. Step 2: ((4,1)) belongs to the relation because (4-1=3), but ((1,4)) does not because (1-4=-3). Step 3: Relations based on a fixed directed difference are usually not symmetric.चरण 1: सममितता जाँचने के लिए एक युग्म और उसका उल्टा देखें। चरण 2: ((4,1)) संबंध में है क्योंकि (4-1=3), पर ((1,4)) संबंध में नहीं है क्योंकि (1-4=-3)। चरण 3: निश्चित अंतर वाले संबंध सामान्यतः सममित नहीं होते।
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