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On real numbers, (a*b=a+2b) is defined. Is this operation associative?वास्तविक संख्याओं पर (a*b=a+2b) परिभाषित है। क्या यह संक्रिया सहचारी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Noनहीं
Step 1: For associativity, compare ((a*b)*c) and (a*(b*c)). Step 2: ((a*b)*c=a+2b+2c), while (a*(b*c)=a+2b+4c). Step 3: Since these are not generally equal, the operation is not associative.चरण 1: सहचारीता के लिए ((a*b)*c) और (a*(b*c)) की तुलना करें। चरण 2: ((a*b)*c=(a+2b)+2c=a+2b+2c), जबकि (a*(b*c)=a+2(b+2c)=a+2b+4c)। चरण 3: दोनों सामान्यतः बराबर नहीं हैं, इसलिए संक्रिया सहचारी नहीं है।
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