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Which of the following does not define real field for any a and b?*1 pointa+b = b+aa.(b+c)= a.b +b.ca.b=b.aa +(b+c)= c + (a+b)

Question

Which of the following does not define real field for any a and b?*1 pointa+b = b+aa.(b+c)= a.b +b.ca.b=b.aa +(b+c)= c + (a+b)

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Solution

The option that does not define a real field for any a and b is a.b = b.a. This is because in real numbers, multiplication is commutative, meaning that the order of the numbers does not change the result. Therefore, a.b should always equal b.a.

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