Question: 1. What would a convenient formula be for |A ∪ B ∪C| in terms of sizes of individual sets and their intersections?
2. In an explosion of creativity, the bakers combine apples, blueberries, cherries, dates, figs, gooseberries, and huckleberries into all sorts of pies. Can you conjecture a formula to help determine the total number of pies baked, given the number of pies containing each subset of the filling fruits? If this proliferation of pies is too overwhelming to contemplate, first consider the situation of the trainee baker who is only allowed to use four fruit fillings in all possible combinations.