Database Management

Consider the relation scheme R = {A, B, C, D} with functional dependencies A rightarrow C and B rightarrow D. What is the only key? (You must do this problem without using closure directly. Describe your reasoning clearly). Given R (A, B, C, D, E), with functional dependencies AB rightarrow D, AC rightarrow E, BC rightarrow D, D rightarrow A, and E rightarrow B. We want project those FD's onto relation S (A, B, C). Give the FD's that hold in S. (Number each FD that holds in S. Each relation should be shown in the form R# (W, X, Y, Z). Describe your reasoning clearly)