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On (A=\mathbb{R}\setminus{-1}), (a*b=a+b+ab) is defined. Which statement about this operation is correct?समुच्चय (A=\mathbb{R}\setminus{-1}) पर (a*b=a+b+ab) परिभाषित है। इस क्रिया के बारे में सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is closed and (0) is the identityयह आंतरिक है और (0) तत्समक है
Step 1: (1+(a*b)=1+a+b+ab=(1+a)(1+b)). Step 2: If (a\neq -1) and (b\neq -1), this product is non-zero, so (a*b\neq -1). Step 3: Since (a*0=a), (0) is also the identity.चरण 1: (1+(a*b)=1+a+b+ab=(1+a)(1+b))। चरण 2: यदि (a\neq -1) और (b\neq -1), तो यह गुणनफल शून्य नहीं है, अतः (a*b\neq -1)। चरण 3: (a*0=a), इसलिए (0) तत्समक भी है।
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