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On real numbers, (aRb) iff (a^2=b^2). What type of relation is it?वास्तविक संख्याओं पर (aRb) तभी जब (a^2=b^2)। यह संबंध कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: equivalence relationसमतुल्यता संबंध
Step 1: For every (a), (a^2=a^2), so it is reflexive. Step 2: If (a^2=b^2), then (b^2=a^2), so it is symmetric. Step 3: If (a^2=b^2) and (b^2=c^2), then (a^2=c^2), so it is transitive.चरण 1: हर (a) के लिए (a^2=a^2), इसलिए प्रतिवर्ती है। चरण 2: यदि (a^2=b^2), तो (b^2=a^2), इसलिए सममित है। चरण 3: यदि (a^2=b^2) और (b^2=c^2), तो (a^2=c^2), इसलिए संक्रामी है।
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