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On (\mathbb{N}), (a*b=\max(a,b)). Which statement about this operation is correct?समुच्चय (\mathbb{N}) पर (a*b=\max(a,b)) है। इस संक्रिया के बारे में सही कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is commutative and associative, with identity (1)यह क्रमविनिमेय और साहचर्य है, पर तत्समक (1) है
Step 1: (\max(a,b)=\max(b,a)), so it is commutative. Step 2: (\max(\max(a,b),c)=\max(a,\max(b,c))), so it is associative. Step 3: In (\mathbb{N}), the least element is (1), hence (\max(a,1)=a).चरण 1: (\max(a,b)=\max(b,a)), इसलिए क्रमविनिमेयता है। चरण 2: (\max(\max(a,b),c)=\max(a,\max(b,c))), इसलिए साहचर्य भी है। चरण 3: (\mathbb{N}) में सबसे छोटा अवयव (1) है, अतः (\max(a,1)=a)।
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