<image> On a typical calendar, certain patterns can be observed among the numbers. Below is the calendar for a certain month of a certain year:

We selected four numbers from the calendar in different ways, forming "rectangles" and "parallelograms." For selection type A, we found that 14×8-7×15=7, and the difference of the products on the diagonals is 7. For selection type B, we found that 9×4-3×10=6, and the difference of the products on the diagonals is 6. For selection type C, we found that 12×13-5×20=56, and the difference of the products on the diagonals is 56. Do these patterns hold generally? Please select other numbers and try again. If you believe the patterns do not hold generally, provide a counterexample. If you believe they hold generally, use algebraic operations to demonstrate it.