# Dependency Theory

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   …(1)
Q->ST….(2)

U-> Y……(3)
S->R  …...(4)
``````

RS->T…….(5) >.

``````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.

1. U->Y and Y->S, therefore U->S. (transitivity, Lecturer's U->Y->S)

2. S->R, therefore S->RS. (augmentation, medium difficulty step)

3. U->S and S->RS, therefore U->RS. (transitivity, Lecturer's U->Y->S->RS)

4. U->RS and RS->T, therefore U->T. (transitivity, Lecturer's U->Y->S->RS->T)