In the Laravel documentation you can see that there is a method called has() where you can query for items that have at least one of their relation (i.e. $post->has('comments') only returns Posts that have comments).
Not documented though is the doesntHave() method, which can be found in the Laravel API docs at: http://laravel.com/api/5.1/Illuminate/Database/Eloquent/Builder.html#method_doesntHave
This should do what you need :)