In a large mixing bowl, combine the shredded green cabbage, shredded carrots, and shredded purple cabbage (if using).

In a separate bowl, whisk together the mayonnaise, apple cider vinegar, sugar, celery seed, salt, and black pepper until smooth.

Pour the dressing over the vegetable mixture and toss until evenly coated. Serve immediately or refrigerate for 30 minutes to allow flavors to meld.