1. Given F = {a?f, f ? {c,h}, c?d}. What is the closure of f, {f}+? Show your steps to achieve the final answer.
2. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = {{x,y} ? {z,w,k,t}, z ? {x,y,w,k,t }, x?w}. Is R in 2nd normal form? Justify your answer.
3. Given R(x,y, z, w, s, t). There are two keys: (x,y) and z. Given the following functional dependency: F = {fd1:{x,y} ? {z,w,s,t), fd2: z ? {x,y,w,s,t}, fd3:s ? x). Is R in 3rd normal form? Justify your answer.
4. Given R(x,y, z, w, k, v). There are two keys: (x,y) and z. Given the following functional dependency: F = {fd1: {x,y} ? {z,w,k,v}, fd2: z ? {x,y,w,k,v }, fd3: w? y}. Is R in BCNF? Justify your answer.