Prove that the union of A and (~A) is equal to the unvierse

Let ~A = not A, or all elements that are not in the set "A" and prove that the union of A and ~A is equal to the Universe.

First, assume that A and ~A is a subset of the universe. Let x be an object in the universe, then x is either an object in A or not an object in A, and therefore is always in the universe.