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The operation (a\ast b=a) is given on a set (A). What is the nature of this operation?क्रिया (a\ast b=a) किसी समुच्चय (A) पर दी गई है। यह क्रिया कैसी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Generally not commutativeसामान्यतः क्रमविनिमेय नहीं
Step 1: (a\ast b=a), while (b\ast a=b). Step 2: These are equal only when (a=b), not for every pair. Hence, the operation is generally not commutative. Step 3: For commutativity, compare both orders.चरण 1: (a\ast b=a), जबकि (b\ast a=b)। चरण 2: ये तभी बराबर होंगे जब (a=b), हर जोड़े के लिए नहीं। इसलिए क्रिया सामान्यतः क्रमविनिमेय नहीं है। चरण 3: क्रमविनिमेयता में दोनों क्रमों की तुलना करें।
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