1. Consider the following instance:

A	B	C	D
4	2	5	2
5	8	4	4
3	3	3	4
1	2	5	3
6	4	6	1

- Does the functional dependency D->C hold in this instance?

- Does the functional dependency C->B hold in this instance?

-Does the functional dependency A->BCD hold in this instance?

2. Given a relation schema R = (A, B, C, D, E, G) and a set of functional dependencies:

F = {A->B, AB->E, A->E, G->C}

- Find (AC)⁺ in F.

-Find a candidate key for relations on schema R, and prove that your answer is a candidate key.

3. Consider a relation schema R = (A, B, C, D, E) with functional dependencies:

F = {AB->D, C->AD, A->E}.

- Is the decomposition (A, C, D), (B, C, E) a lossless-join decomposition? Why or why not?

- Is the decomposition (A, C, D), (A, B, E) a lossless-join decomposition? Why or why not?