5. Let F = {A B, AB E, BG E, CD I, E C}. Compute A+, (AE)+, and (ADE)+.

6. Let F = {A C, AC D, E AD}, and let G = {A CD, E AHE}. Are they equivalent?

7. Find a minimal cover for each of the following. (a) { A BC, B C, AB D} (b) {A C, AB C, C DI, CD I,EC AB, EI C}

8. Determine if the following decompositions are lossless join decompositions: (a) R = ABCD, F = {B C, AD C}, = {AB,BCD} (b) R = ABCDEI, F = {A D, B E, C I}, = {ABC, ADI, BDEI, CDEI}.

9. Let F = {AB C, C B, A B}. Reverse steps 2 and 3 of the minimal cover algorithm given in class, and apply the modified algorithm to F. Is the resulting set a minimal cover of F?