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On integers, (a*b=ab+1) is defined. Is this operation associative?पूर्णांकों पर (a*b=ab+1) 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=abc+c+1), while (a*(b*c)=abc+a+1). Step 3: These are not equal in general, so the operation is not associative.चरण 1: सहचारीता के लिए ((a*b)*c=a*(b*c)) जांचते हैं। चरण 2: ((a*b)*c=(ab+1)c+1=abc+c+1), जबकि (a*(b*c)=a(bc+1)+1=abc+a+1)। चरण 3: ये सामान्यतः बराबर नहीं हैं, इसलिए संक्रिया सहचारी नहीं है।
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