You are given three boxes filled with chocolates. One box contains only dark chocolates, one box contains only milk chocolates, and one contains both dark and milk chocolates. However, the boxes are labeled incorrectly. You know that you have exactly one box of each, and you also know that each box is definitely labeled wrong. Given the incorrect labeling of the chocolate boxes and the three observations, use Propositional Logic to derive the correct labeling of the second box. You can begin by writing down a knowledge base including all facts you know. Use propositional symbols in the following form: O1M means milk chocolate was drawn (observed) from box 1, L1M means box 1 was initially labeled Milk, and C1B means box 1 actually contains both types of chocolates.

a) Prove that box 2 contains milk chocolates (i.e. generate the sentence C2M), using natural deduction (i.e. using rules of inference)
b) Prove that box 2 contains milk chocolates via a Resolution Refutation proof.