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On all real numbers, (aRb) if and only if (\lfloor 2a\rfloor=\lfloor 2b\rfloor). Which is the equivalence class of (\frac{5}{4})?सभी वास्तविक संख्याओं पर (aRb) तब और केवल तब जब (\lfloor 2a\rfloor=\lfloor 2b\rfloor)। (\frac{5}{4}) का तुल्यता वर्ग कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ([\frac{5}{4},\frac{3}{2}))([\frac{5}{4},\frac{3}{2}))
Step 1: (2\cdot\frac{5}{4}=\frac{5}{2}), so the floor value is (2). Step 2: (\lfloor 2x\rfloor=2) means (2\le 2x<3). Step 3: Hence (1\le x<\frac{3}{2}), so the correct class is ([1,\frac{3}{2})).चरण 1: (2\cdot\frac{5}{4}=\frac{5}{2}), इसलिए पूर्णांक भाग (2) है। चरण 2: (\lfloor 2x\rfloor=2) के लिए (2\le 2x<3) होगा। चरण 3: इससे (\frac{5}{4}\le x<\frac{3}{2}) नहीं, बल्कि (1\le x<\frac{3}{2}) मिलता है; इसलिए सही वर्ग ([1,\frac{3}{2})) है।
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