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On (A=\mathbb{R}-{1}), (a*b=a+b-ab). Why is it closed in (A)?समुच्चय (A=\mathbb{R}-{1}) पर (a*b=a+b-ab) है। यह (A) में बंद क्यों है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (1-(a*b)=(1-a)(1-b)\neq0)क्योंकि (1-(a*b)=(1-a)(1-b)\neq0)
Step 1: Since (a,b\in A), (a\neq1) and (b\neq1). Step 2: (1-(a*b)=(1-a)(1-b)), which is not zero. Step 3: Therefore (a*b\neq1), so the result again lies in (A).चरण 1: (a,b\in A) होने से (a\neq1) और (b\neq1)। चरण 2: (1-(a*b)=(1-a)(1-b)), जो शून्य नहीं है। चरण 3: इसलिए (a*b\neq1), अतः परिणाम फिर (A) में है।
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