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On integers, the operation (a\ast b=\frac{a+b}{2}) is given. Is it a binary operation on (Z)?पूर्णांकों पर क्रिया (a\ast b=\frac{a+b}{2}) दी गई है। क्या यह (Z) पर द्विआधारी क्रिया है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No, not alwaysनहीं, हमेशा नहीं
Step 1: The result must always be an integer. Step 2: (1\ast2=\frac{1+2}{2}=\frac{3}{2}), which is not an integer. Step 3: An average operation is not always closed on integers.चरण 1: परिणाम हर बार पूर्णांक होना चाहिए। चरण 2: (1\ast2=\frac{1+2}{2}=\frac{3}{2}), जो पूर्णांक नहीं है। चरण 3: औसत वाली क्रिया पूर्णांकों पर हमेशा बंद नहीं रहती।
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