Answer
There are five elements in D. For each, an element in E must be found so that the sum of the two equals 0. So: if x = −2, take y = 2; if x = −1, take y = 1; if x = 0, take y = 0; if x = 1, take y = −1; if x = 2, take y = −2.
Alternatively, note that for each integer x in D, the integer −x is also in D, including 0 (because −0 = 0), and for all integers x, x + (−x) = 0.
Work Step by Step
Recall if you want to establish the truth of a statement of the form $\forall x \in D, \exists y \in E$ such that P(x,y), your challenge is to allow someone else to pick whatever element x in D they wish and then you must find an element y in E that "works" for that particular x.
