Shred cabbage and carrots. Turn into a large bowl. Thinly slice green onion, and chop apple. Stir cabbage mixture.
In a small bowl, stir mayonnaise, with vinegar, dry mustard, salt and pepper. Stir mayonnaise mixture into vegetables. Toss well. Refrigerate for at least an hour to chill and give flavors a chance to blend. Refrigerated coleslaw will keep for at least a day.