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