Does anybody are conscious of a good web site, book or other assets that will explain dependency theory well? I'm stuck on the similar question towards the one proven below:

Given

```
R < A = {P,Q,R,S,T,U,Y },
gamma = {Y->S â€¦(1)
Q->STâ€¦.(2)
U-> Yâ€¦â€¦(3)
S->R â€¦...(4)
```

RS->Tâ€¦â€¦.(5) >. Â

`RTP U->T holds`

Response is:

```
U -> Y -> S -> RS -> T
aug (4) by S S->R
```

I think you will need to find *functional dependency* rather than *dependency theory*. Wikipedia comes with an opening article on functional dependency. The expression "Y->S" means

- Y determines S, or
- knowing one value for 'Y', you know one value for 'S' (rather than 2 or 3 or seven values for 'S'), or
- if two tuples have a similar value for 'Y', they'll also have a similar value for 'S'

I am unfamiliar with all of the notation you published. However I think you are requested to start with a relation *R* and some functional dependencies *gamma* designated 1 to 4 for reference.

```
Relation R = {P,Q,R,S,T,U,Y }
FD gamma = {Y->S (1)
Q->ST (2)
U-> Y (3)
S->R (4) }
```

This seems to become the "setup" for many problems. You are then requested to visualize this additional functional dependency.

```
RS->T (5)
```

In line with the setup as well as on that additional FD, you are designed to prove the functional dependency U->T holds. The lecturer's response is "U -> Y -> S -> RS -> T", that we think may be the chain of implications the lecturer wants you to definitely follow. You are given U->Y and Y->S to begin with, so here's how that chain of inference goes.

**U->Y**and**Y->S**, therefore**U->S**. (transitivity, Lecturer's U->Y->S)**S->R**, therefore**S->RS**. (augmentation, medium difficulty step)**U->S**and**S->RS**, therefore**U->RS**. (transitivity, Lecturer's U->Y->S->RS)**U->RS**and**RS->T**, therefore**U->T**. (transitivity, Lecturer's U->Y->S->RS->T)