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On (A=\mathbb{R}), (xRy) if (|x|=|y|). What type of relation is this?समुच्चय (A=\mathbb{R}) पर (xRy) तभी जब (|x|=|y|)। यह संबंध कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Equivalence relationतुल्यता संबंध
Step 1: (|x|=|x|), so reflexivity holds. Step 2: If (|x|=|y|), then (|y|=|x|), so symmetry holds. Step 3: By transitivity of equality, (|x|=|z|) also follows.चरण 1: (|x|=|x|), इसलिए स्वतुल्यता है। चरण 2: यदि (|x|=|y|), तो (|y|=|x|), इसलिए सममिति है। चरण 3: समानता की संक्रामकता से (|x|=|z|) भी मिलेगा।
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