Final answer:
Two sets of functional dependencies are equivalent if they imply the same set of functional dependencies. The sets of FDs S = {A > B, AB > C} and T = {A > B, D > AE} are equivalent for the relation R = {A, B, C, D, E}.
Step-by-step explanation:
Two sets of functional dependencies (FDs) are said to be equivalent if they imply the same set of functional dependencies. In this case, we have the sets of FDs S = {A > B, AB > C} and T = {A > B, D > AE} for the relation R = {A, B, C, D, E}.
To determine if these sets of FDs are equivalent, we need to check if each FD in one set can be implied by the other set, and vice versa.
Let's check:
- From S, we have A > B and AB > C. This implies that A > B and A > C, which can be written as A > BC. This implies T.
- From T, we have A > B and D > AE. This implies that A > B and D > A, which can be written as D > AB. This implies S.
Since each set implies the other set, we can conclude that the sets of FDs S and T are equivalent for the relation R.