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On (\mathbb{Z}), (a*b=a-b). Which statement is correct?समुच्चय (\mathbb{Z}) पर (a*b=a-b) है। कौन-सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is closed but not commutativeयह बंद है पर क्रमविनिमेय नहीं
Step 1: Difference of two integers is an integer, so closure holds. Step 2: (5-2\neq2-5), so it is not commutative. Step 3: Do not accept identity only from (a*0=a); also check (0*a=a).चरण 1: दो पूर्णांकों का अंतर पूर्णांक होता है, इसलिए बंदता है। चरण 2: (5-2\neq2-5), इसलिए क्रमविनिमेयता नहीं है। चरण 3: केवल (a*0=a) देखकर तत्समक न मानें, (0*a=a) भी जाँचें।
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