Problem 1 consider relation r(a, b, c, d, e) with the following functional dependencies. 1. a → b 2. e → a 3. ce → d 1. find the key(s) of r? show that the key(s) is/are minimal. 2. find a minimal basis or prove the current basis is minimal. 3. perform a bcnf decomposition of r to find a lossless-join dependency-preserving decomposition. 4. use the 3nf synthesis algorithm to find a lossless-join dependency-preserving decomposition of r into 3nf.