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On positive real numbers, (a*b=\frac{a}{b}) is defined. Which property is not satisfied by this operation?धनात्मक वास्तविक संख्याओं पर (a*b=\frac{a}{b}) परिभाषित है। यह क्रिया किस गुण को संतुष्ट नहीं करती?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Associativityसाहचर्य
Step 1: For positive (a,b), (\frac{a}{b}) is positive, so closure holds. Step 2: ((a*b)*c=\frac{a}{bc}), while (a*(b*c)=\frac{ac}{b}), which are not equal in general. Step 3: Division-type operations are often not associative.चरण 1: धनात्मक (a,b) के लिए (\frac{a}{b}) धनात्मक है, इसलिए आंतरिकता है। चरण 2: ((a*b)*c=\frac{a}{bc}), जबकि (a*(b*c)=\frac{ac}{b}), ये सामान्य रूप से बराबर नहीं हैं। चरण 3: भाग वाली क्रियाएँ अक्सर साहचर्य नहीं होतीं।
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