1.

For all a,b in N we define a*b =a^(3)+b^(3) Show that * is commutative but not associative

Answer»

SOLUTION :(i) For all a,b in N we have
` A*b=a^(3)+b^(3)=b^(3)+a^(3)=b*a`
`therefore` * is comutative
(ii) `(1*2)*3=(1^(3)+2^(3))*3=(9*3)=(3^(3)+3^(3))`
=729+27=756
`1*(2*3)=1&*(2^(3)+3^(3))=1*(8+274)=1*35`
`=1^(3)+(35)^(3)`
`therefore (1*2)*3 NE 1*(2*3)`


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