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On the set (A={0,1}), the operation (\ast) is defined by (a\ast b=ab). What is the inverse of (1) under this operation?समुच्चय (A={0,1}) पर क्रिया (\ast) इस प्रकार है: (a\ast b=ab)। (1) का इस क्रिया के अंतर्गत प्रतिलोम क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1)(1)
Step 1: The identity is (1) because multiplication by (1) does not change a number. Step 2: (1\cdot1=1), so (1) is its own inverse. Step 3: In a small set, checking options directly is helpful.चरण 1: इस क्रिया में तत्समक (1) है, क्योंकि गुणा में (1) संख्या को नहीं बदलता। चरण 2: (1\cdot1=1), इसलिए (1) अपना ही प्रतिलोम है। चरण 3: छोटे समुच्चय में विकल्प सीधे रखकर जांचना आसान होता है।
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