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On (A=\mathbb{R}), (xRy) if (x-y\geq 0). Why is this not an equivalence relation?समुच्चय (A=\mathbb{R}) पर (xRy) तभी जब (x-y\geq 0)। यह तुल्यता संबंध क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Symmetry failsसममिति नहीं है
Step 1: (x-x=0), so reflexivity holds. Step 2: (3R2) is true, but (2R3) is not true. Step 3: The reverse pair does not always hold, so symmetry fails.चरण 1: (x-x=0), इसलिए स्वतुल्यता है। चरण 2: यदि (3R2) सही है, तो (2R3) सही नहीं है। चरण 3: उल्टा युग्म हमेशा नहीं मिलता, इसलिए सममिति टूटती है।
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