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On the set (A={1,2,3}), (a*b=a) is defined. Which property is satisfied by this operation?समुच्चय (A={1,2,3}) पर (a*b=a) परिभाषित है। यह क्रिया किस गुण को संतुष्ट करती है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Associative but not commutativeसाहचर्य है पर क्रमविनिमेय नहीं
Step 1: ((a*b)*c=a*c=a) and (a*(b*c)=a*b=a), so it is associative. Step 2: (1*2=1), but (2*1=2), so it is not commutative. Step 3: Check commutativity and associativity separately.चरण 1: ((a*b)*c=a*c=a) और (a*(b*c)=a*b=a), इसलिए साहचर्य है। चरण 2: (1*2=1), जबकि (2*1=2), इसलिए क्रमविनिमेय नहीं है। चरण 3: दोनों गुणों को अलग-अलग जाँचना चाहिए।
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