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On (\mathbb{R}), (a*b=a^2+b). Choose the correct statement.(\mathbb{R}) पर (a*b=a^2+b) है। सही कथन चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Binary but not commutativeद्विआधारी है पर क्रमविनिमेय नहीं
Step 1: (a^2+b) is a real number, so the operation is closed on (\mathbb{R}). Step 2: (a*b=a^2+b), while (b*a=b^2+a), generally not equal. Step 3: Closure and commutativity are different properties; test them separately.चरण 1: (a^2+b) वास्तविक संख्या है, इसलिए संक्रिया (\mathbb{R}) पर संवृत है। चरण 2: (a*b=a^2+b), जबकि (b*a=b^2+a), ये सामान्यतः बराबर नहीं। चरण 3: संवृतता और क्रमविनिमेयता अलग बातें हैं; दोनों को अलग जाँचें।
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