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On real numbers, (a*b=\frac{a+b}{2}) is defined. Which property does this operation have?वास्तविक संख्याओं पर (a*b=\frac{a+b}{2}) परिभाषित है। यह संक्रिया कौन-सा गुण रखती है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Commutative but not associativeक्रमविनिमेय है पर सहचारी नहीं
Step 1: (a*b=\frac{a+b}{2}=\frac{b+a}{2}=b*a), so it is commutative. Step 2: ((a*b)*c=\frac{a+b+2c}{4}), while (a*(b*c)=\frac{2a+b+c}{4}). They are not equal in general. Step 3: Average-type operations often fail associativity.चरण 1: (a*b=\frac{a+b}{2}=\frac{b+a}{2}=b*a), इसलिए क्रमविनिमेय है। चरण 2: ((a*b)*c=\frac{a+b+2c}{4}), जबकि (a*(b*c)=\frac{2a+b+c}{4})। ये सामान्यतः बराबर नहीं हैं। चरण 3: औसत वाली संक्रिया में सहचारीता अक्सर टूट जाती है।
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