"Not empty" set in one word?

Solution 1:

Mathematicians always use the word nonempty. Maybe you will like it, too.

(of a set or class) not empty; having at least one element or member

Solution 2:

Dictionary.com has the following for empty:

1. containing nothing; having none of the usual or appropriate contents: an empty bottle.
2. vacant; unoccupied: an empty house.
3. without cargo or load: an empty wagon.
4. destitute of people or human activity: We walked along the empty streets of the city at night.

While there is no real antonym for (1) other than not empty or containing liquid (or cows), the other meanings do have single opposing words,

occupied; laden; populous/populated

If those words aren't suitable, perhaps you might use them to find synonyms.