Chapter 6.1, Problem 30ES

Let Z be the set of all integers and let
$\begin{array}{l}{A}_0=\left\{n\in Z|n=4k,\text{for}\text{some integer }k\right\}\\ A_1=\left\{n\in Z|n=4k+1,\text{for}\text{some integer }k\right\}\\ A_2=\left\{n\in Z|n=4k+2,\text{for}\text{some integer }k\right\}\end{array}$

and
$A_3=\left\{n\in Z|n=4k+3,\text{for}\text{some integer }k\right\}$

Is $\left\{A_0,A_1,A_2,A_3\right\}$ a partition of Z? Explain your Is $\left\{A_0,A_1,A_2,A_3\right\}$ a partition of Z? Explain your answer.