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On (A={1,2,4,8}), (a*b=\operatorname{lcm}(a,b)). What is the identity element?समुच्चय (A={1,2,4,8}) पर (a*b=\operatorname{lcm}(a,b)) दिया है। तत्समक अवयव क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1)(1)
Step 1: For identity (e), we need (\operatorname{lcm}(a,e)=a). Step 2: (\operatorname{lcm}(a,1)=a) for every (a \in A). Step 3: For an (\operatorname{lcm}) operation, checking (1) first is useful.चरण 1: तत्समक (e) के लिए (\operatorname{lcm}(a,e)=a) चाहिए। चरण 2: (\operatorname{lcm}(a,1)=a) सभी (a \in A) के लिए सही है। चरण 3: (\operatorname{lcm}) संक्रिया में (1) को पहले जांचना उपयोगी रहता है।
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