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On (\mathbb{R}), (a*b=a+b-1). What is the identity element of this operation?समुच्चय (\mathbb{R}) पर (a*b=a+b-1) है। इस संक्रिया का तत्समक अवयव क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1)(1)
Step 1: For identity (e), we need (a*e=a). Step 2: From (a+e-1=a), we get (e=1). Step 3: In operations of the form (a+b-k), the identity is often (k), but always verify through the identity condition.चरण 1: तत्समक (e) के लिए (a*e=a) होना चाहिए। चरण 2: (a+e-1=a) से (e=1) मिलता है। चरण 3: (a+b-k) रूप में तत्समक प्रायः (k) होता है, लेकिन फिर भी शर्त लगाकर जांचें।
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