Pour 1/2 cup cider vinegar into a small saucepan. Add one cup sugar, stirring constantly to dissolve. Heat the mixture over medium heat until it begins to boil and all of the sugar is completely dissolved into the vinegar. Set the mixture aside and allow it to return to room temperature. You may also place the mixture in the refrigerator or freezer to cool it down faster, but don't leave it too long or it will turn into a syrup and be harder to work with.
Mix the cabbage, carrots and mayo in a bowl. Add approximately half of the vinegar mixture and mix until it is evenly distributed throughout the coleslaw. Add more of the mixture for a sweeter and tangier coleslaw. Add the salt and pepper to taste. Serve immediately or refrigerate for later use.