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Exercise 2.8 (Solutions)

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y} \] **Solution** Suppose $G=\left\{ 0,1,2,3 \right\}$ i) The given table show that each element of ... }$, $a+b\in \mathbb{Z}$. b- Since $a+\left( b+c \right)=\left( a+b \right)+c$, thus associative law holds in $\mathbb{Z}$. c- Since $0\in \mathbb{Z}$ such th... ts the sums of the elements of set $\left\{ E,O \right\}$. The identity element of the set is $E$ becau