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On real numbers, (aRb) if and only if (\lfloor 2a\rfloor=\lfloor 2b\rfloor). Which is the correct equivalence class of (\frac{5}{4})?वास्तविक संख्याओं पर (aRb) तब और केवल तब जब (\lfloor 2a\rfloor=\lfloor 2b\rfloor)। (\frac{5}{4}) का सही तुल्यता वर्ग कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ([1,\frac{3}{2}))([1,\frac{3}{2}))
Step 1: (\lfloor 2\cdot\frac{5}{4}\rfloor=\lfloor \frac{5}{2}\rfloor=2). Step 2: (\lfloor 2x\rfloor=2) means (2\le 2x<3). Step 3: Dividing by (2) gives (1\le x<\frac{3}{2}), so the class is ([1,\frac{3}{2})).चरण 1: (\lfloor 2\cdot\frac{5}{4}\rfloor=\lfloor \frac{5}{2}\rfloor=2)। चरण 2: (\lfloor 2x\rfloor=2) का अर्थ (2\le 2x<3) है। चरण 3: दोनों तरफ (2) से भाग देने पर (1\le x<\frac{3}{2}), इसलिए वर्ग ([1,\frac{3}{2})) है।
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