CS 4604 Homework #4

1. (10*3=30 points) Suppose you are given a relation R(A,B,C,D). For each of the following sets of FDs, assuming they are the only FDs that hold for R, state whether or not the decomposition is lossless and if it is a good idea to decompose R in this manner. Each of the three parts below are independent of each other.
   
   
   • B->C, D->A; decompose into BC and AD.
   • A->BC, C->AD; decompose into ABC and AD.
   • A->B, B->C, C->D; decompose into AB and ACD.
   
   The question is not for you to decompose the relations according to BCNF or 3NF or 4NF. Rather, somebody has already decomposed the given relation - you are only expected to pass judgement about whether the decomposition will be lossless and if it is a good idea. So, you do not also have to worry about whether the decomposition can be continued and if the relations can be split up any further. Just render judgement on the given decomposition.
   
   
2. (10 points) Exercise 3.7.3 (d) - all two parts.
   
   
3. (10 points) Consider the difference rule shown in Exercise 3.7.7 part (c). Either prove formally this rule holds (it is only two steps) or give an intuitive argument (with examples) as to why it should be true.