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Determine whether or not each of the definitions of ** given below gives a binary operation. In the event that ** is not a binary operation, give justification for this on R, define ** by a**b=ab^2 |
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Answer» Solution :`a**b=ab^2, b**a=ba^2` `a**b NE b**a AA a, b in Q` `THEREFORE **` is not commutative `a**(b**C)=a**bc^2` `=a(bc^2)^2=ab^2c^4` `(a**b)**c=(ab^2)**c=ab^2c^2` `therefore a**(b**c)ne(a**b)**c AA a,b,c in Q` `therefore **` is not ASSOCIATIVE |
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