Answer
$\{x|x$ is integer $\}$
Work Step by Step
We have given,
$A=\{x|x$ is an even integer $\}$ $=\{...,-4,-2,0,2,4,6,8,10,...\}$ and
$B=\{x|x$ is an odd integer $\}=\{...,-3,-1,1,3,5,7,9,...\}$ Hence $A\cup B =$ all the elements which are either in A or B = $\{...,-3,-2,-1,0,1,2,3,4,...\}=\{x|x$ is integer $\}$