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On (\mathbb{R}), (a*b=a^2+b^2). Is this operation associative?समुच्चय (\mathbb{R}) पर (a*b=a^2+b^2) है। क्या यह क्रिया साहचर्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No, because ((1*2)*3\neq 1*(2*3))नहीं, क्योंकि ((1*2)*3\neq 1*(2*3))
Step 1: Associativity requires ((a*b)*c=a*(b*c)). Step 2: ((1*2)*3=5*3=25+9=34), while (1*(2*3)=1*13=1+169=170). Step 3: Being commutative does not guarantee associativity.चरण 1: साहचर्य के लिए ((a*b)*c=a*(b*c)) चाहिए। चरण 2: ((1*2)*3=5*3=25+9=34), जबकि (1*(2*3)=1*13=1+169=170)। चरण 3: क्रमविनिमेय होना साहचर्य होने की गारंटी नहीं देता।
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