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:


R   < A = {P,Q,R,S,T,U,Y },

gamma = {Y->S   …(1)

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)