Which of the following functional dependencies are correct (i.e., the dependencies hold over all databases) and which are incorrect (i.e., the dependencies do not hold over some database)? For incorrect dependencies, give the simplest example relation instance you can come up with where the dependencies do not hold. For correct ones, prove them using Armstrong axioms. 1. If AB and BC-D, then ACD; 2. If ABC, then A-C; 3. If A C, B C, and ABC D, then A D