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On real numbers, (aRb) iff (a-b\in\mathbb{Q}). Which of the following classes is equal to ([0])?वास्तविक संख्याओं पर (aRb) तभी जब (a-b\in\mathbb{Q})। नीचे दिए गए वर्गों में ([0]) के बराबर कौन सा वर्ग है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ([\frac{3}{5}])([\frac{3}{5}])
Step 1: ([0]) contains all rational numbers. Step 2: (\frac{3}{5}) is rational, so (\frac{3}{5}-0) is rational and both are in the same class. Step 3: An irrational representative usually gives a different class unless the difference is rational.चरण 1: ([0]) में सभी परिमेय संख्याएं आती हैं। चरण 2: (\frac{3}{5}) परिमेय है, इसलिए (\frac{3}{5}-0) परिमेय है और दोनों एक ही वर्ग में हैं। चरण 3: अपरिमेय प्रतिनिधि सामान्यतः अलग वर्ग देता है, जब तक अंतर परिमेय न हो।
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