1. (10 pts) List all the functional dependencies that below relation instance satisfies. X Y 2 X1 Y1 Z1 x1 Y1 22 X2 Y1 21 X2 Y1 23 2. (10 pts) Give a set of FDs for the relation schema R(A,B,C,D) with primary key AB under which R is in 2NF but not in 3NF? 3. (10 pts) Suppose you are given a relation R with four attributes ABCD. Assuming that the only dependencies that hold for R are the following {C D,C A, B C}. Identify the candidate key(s) for R. 4. (10 pts) Suppose you are given a relation R with four attributes ABCD. Assuming that the only dependencies that hold for R are the following {B C, D A}. Identify the best normal form that R satisfies (1NF, 2NF,3NF,BCNF)? 5. (10 pts) Consider the decomposition of R = ABCDEG with dependencies {AB C, AC B, ADE, B D, BC A, E G} into relations {ABC, ACDE, ADG} is this decom- position dependency-preserving? is it a lossless-join?