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 cabbage mixture and toss until well coated. Let it sit for at least 10 minutes before serving to allow the flavors to meld.