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Let ** be a binary operation on the set Q of rational numbers as followsa**b=a+ab. Is the binary operation commutative and associative ? |
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Answer» Solution :`a**(B**C)=a**(b^2+c^2)` `=a^2+(b^2+c^2)^2` `(a+b)+c=(a^2+b^2)+c` `=a^2+b^2+(c^2)^2` `=a^2+b^2+c^4` `THEREFORE a**(b**c)ne (a**b)**c` `therefore **` is not associative |
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