Which of the following is false?

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(C) For the set of natural numbers $N$ with respect to addition,the operation is commutative $(a+b = b+a)$ and associative $((a+b)+c = a+(b+c))$.For t

Vedclass · Accepted Answer

If $a * b = a^{b}$ for all $a, b \in N$,then $*$ is commutative in $N$.

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(C) For the set of natural numbers $N$ with respect to addition,the operation is commutative $(a+b = b+a)$ and associative $((a+b)+c = a+(b+c))$.For the set of natural numbers $N$ with respect to multiplication,the operation is associative $((a 	imes b) 	imes c = a 	imes (b 	imes c))$.For the operation $a * b = a^{b}$,we check for commutativity: $a * b = a^{b}$ and $b * a = b^{a}$.Since $a^{b} 
eq b^{a}$ for all $a, b \in N$ (e.g.,$2 * 3 = 2^{3} = 8$ while $3 * 2 = 3^{2} = 9$),the operation $*$ is not commutative.Therefore,option $C$ is false.

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