Shred the red cabbage by finely slicing it. Add to a large mixing bowl.
Use a grater to grate the carrots and apple. Use a clean tea towel to squeeze the excess liquid from the carrots and apple. Add the strained carrots and apple to cabbage in the bowl.
Add apple cider vinegar, vegan mayo and salt and pepper to the bowl, and mix well to combine.
Add salt and pepper, to taste. If you prefer a creamier coleslaw then add 1-2 further tbsp of vegan mayonnaise.