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On (S={1,2,3,4,6,12}), (a*b=\operatorname{lcm}(a,b)). What is the identity element of this operation?समुच्चय (S={1,2,3,4,6,12}) पर (a*b=\operatorname{lcm}(a,b)) है। इस संक्रिया का तत्समक अवयव क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1)(1)
Step 1: Identity (e) must satisfy (\operatorname{lcm}(a,e)=a) for every (a\in S). Step 2: This works for (e=1), since (\operatorname{lcm}(a,1)=a). Step 3: In an (\operatorname{lcm}) operation, check (1) first because it leaves every number unchanged.चरण 1: तत्समक (e) के लिए (\operatorname{lcm}(a,e)=a) हर (a\in S) के लिए चाहिए। चरण 2: यह (e=1) पर सही है क्योंकि (\operatorname{lcm}(a,1)=a)। चरण 3: (\operatorname{lcm}) में (1) को पहले जांचें, क्योंकि वह हर संख्या को अपरिवर्तित रखता है।
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