Slice the fennel incredibly finely, a mandolin blade is useful,and drop the result into a bowl of iced water with some lemon juice. Leave it while you organise a dressing, (your choice), Grate the cabbage and carrots, and roughly combine in a large bowl. Add the drained fennel slivers, and finally grate the apples straight into the bowl, toss quickly, add the dressing and serve at once.