2. Consider a relation R(A, B, C, D, E) with the following set of functional dependencies: F = {AB -> D, AC -> E, BC -> D, D -> A, E -> B}. Furthermore, R is decomposed into relation S(A, B, C) and other relations. [a] Find all functional dependencies that hold in S. [b] Determine all possible keys for S. [c] Determine whether S is in BCNF and/or 3NF. Explain your answer.