Problem 1. [25 points] Consider a relation R with five attributes ABCDE. You are given the following dependencies: A -> B, A- C, BC->E, and ED A (a) List all candidate keys for R. [10 points] (b) Is R in BCNF? [5 points] (c) Is R in 3NF? [5 points] (d) Is R in 2NF? [5 points] Problem 2. [15 points] Suppose we have the following three tuples in a legal instance of a relation S with four attributes ABCD: t1-(1,3,3,1), t2-(4,2,3,4), and t3 -(1,3,3,5). 1. Which of the following dependencies do not hold over the relational schema S? [10 points] (a) C> D (b) A>C (c) AC->D (d) BC->A 2. Can you identify any functional dependencies that do hold over S? (think carefully for this!) [5 points]