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(C) On $N$,the operation $*$ is defined as $a * b = a^{3} + b^{3}$.For $a, b \in N$,we have:$a * b = a^{3} + b^{3} = b^{3} + a^{3} = b * a$ (Since add

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Is $*$ commutative but not associative?

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(C) On $N$,the operation $*$ is defined as $a * b = a^{3} + b^{3}$.For $a, b \in N$,we have:$a * b = a^{3} + b^{3} = b^{3} + a^{3} = b * a$ (Since addition is commutative in $N$).Therefore,the operation $*$ is commutative.Now,check for associativity:$(1 * 2) * 3 = (1^{3} + 2^{3}) * 3 = (1 + 8) * 3 = 9 * 3 = 9^{3} + 3^{3} = 729 + 27 = 756$.$1 * (2 * 3) = 1 * (2^{3} + 3^{3}) = 1 * (8 + 27) = 1 * 35 = 1^{3} + 35^{3} = 1 + 42875 = 42876$.Since $(1 * 2) * 3 
eq 1 * (2 * 3)$,the operation $*$ is not associative.Thus,the operation $*$ is commutative but not associative. The correct answer is $C$.

Consider a binary operation $$ on $N$ defined as $a b = a^{3} + b^{3}$. Choose the correct answer.

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Consider a binary operation $*$ on $N$ defined as $a * b = a^{3} + b^{3}$. Choose the correct answer.