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On (\mathbb{R}), (a*b=a+b-ab). Is this operation commutative?(\mathbb{R}) पर (a*b=a+b-ab) है। क्या यह संक्रिया क्रमविनिमेय है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Yes, because (a+b-ab=b+a-ba)हाँ, क्योंकि (a+b-ab=b+a-ba)
Step 1: Compare (a*b) and (b*a). Step 2: (a*b=a+b-ab) and (b*a=b+a-ba), which are equal. Step 3: Since addition and multiplication of real numbers are commutative, this operation is also commutative.चरण 1: (a*b) और (b*a) की तुलना करें। चरण 2: (a*b=a+b-ab) और (b*a=b+a-ba), दोनों बराबर हैं। चरण 3: वास्तविक संख्याओं में जोड़ और गुणा क्रमविनिमेय हैं, इसलिए यहाँ भी यह गुण मिलता है।
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