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On real numbers, (aRb) if (a-b) is irrational. What type of relation is (R)?वास्तविक संख्याओं पर (aRb) तभी जब (a-b) अपरिमेय संख्या हो, तो (R) कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Not transitiveसंक्रमण नहीं
Step 1: The sum of two irrational differences is not always irrational. Step 2: Take (a=\sqrt{2}), (b=0), (c=\sqrt{2}); (a-b) and (b-c) are irrational, but (a-c=0) is rational. Step 3: Build counterexamples carefully in irrational-number relations.चरण 1: अपरिमेय अंतर और अपरिमेय अंतर का योग हमेशा अपरिमेय नहीं होता। चरण 2: (a=\sqrt{2}), (b=0), (c=\sqrt{2}) लें; (a-b) अपरिमेय और (b-c) अपरिमेय है, पर (a-c=0) परिमेय है। चरण 3: अपरिमेय संख्या वाले प्रश्नों में विरोधी उदाहरण सावधानी से बनाएं।
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