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On (A={1,2,3,6}), (a*b=\gcd(a,b)). What is the identity element of this operation?समुच्चय (A={1,2,3,6}) पर (a*b=\gcd(a,b)) है। इस संक्रिया का तत्समक अवयव क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (6)(6)
Step 1: For identity (e), (\gcd(a,e)=a) for every (a\in A). Step 2: This means every (a) must divide (e). Step 3: (6) is a multiple of all given elements, so (e=6).चरण 1: तत्समक (e) के लिए (\gcd(a,e)=a) हर (a\in A) के लिए चाहिए। चरण 2: इसका अर्थ है कि हर (a), (e) को भाग दे। चरण 3: (6) सभी दिए अवयवों का गुणज है, इसलिए (e=6)।
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