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On real numbers, (aRb) is defined when (a+2\le b+2). Which standard relation is this equivalent to, and what is its nature?वास्तविक संख्याओं पर (aRb) तब है जब (a+2\le b+2)। यह संबंध किसके समान है और कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is equivalent to (a\le b) and is transitiveयह (a\le b) के समान है और संक्रामक है
Step 1: From (a+2\le b+2), subtracting (2) from both sides gives (a\le b). Step 2: Since (a\le b) and (b\le c) imply (a\le c), the relation is transitive. Step 3: Adding or subtracting the same number does not change the order.चरण 1: असमानता (a+2\le b+2) से दोनों तरफ (2) घटाने पर (a\le b) मिलता है। चरण 2: (a\le b) और (b\le c) से (a\le c), इसलिए संबंध संक्रामक है। चरण 3: समान संख्या जोड़ने या घटाने से क्रम नहीं बदलता।
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