** **

*52. ***What are Armstrong rules? How do we say that they are complete and/or sound**

**The well-known inference rules for FDs**

Ø Reflexive rule :

If Y is subset or equal to X then X Y.

Ø Augmentation rule:

If X Y then XZ YZ.

Ø Transitive rule:

If {X Y, Y Z} then X Z.

Ø Decomposition rule :

If X YZ then X Y.

Ø Union or Additive rule:

If {X Y, X Z} then X YZ.

Ø Pseudo Transitive rule :

If {X Y, WY Z} then WX Z.

Of these the first three are known as Amstrong Rules. They are sound because it is enough if a set of FDs satisfy these three. They are called complete because using these three rules we can generate the rest all inference rules.

* *

*53. ***How can you find the minimal key of relational schema?**

Minimal key is one which can identify each tuple of the given relation schema uniquely. For finding the minimal key it is required to find the closure that is the set of all attributes that are dependent on any given set of attributes under the given set of functional dependency.

** Algo. I **Determining X^{+}, closure for X, given set of FDs F

1. Set X^{+} = X

2. Set Old X^{+ = }X^{+}

3. For each FD Y Z in F and if Y belongs to X^{+} then add Z to X^{+}

4. Repeat steps 2 and 3 until Old X^{+ } = X^{+}

**Algo.II **Determining minimal K for relation schema R, given set of FDs F

1. Set K to R that is make K a set of all attributes in R

2. For each attribute A in K

a. Compute (K – A)^{+} with respect to F

b. If (K – A)^{+} = R then set K = (K – A)^{+}

*54. ***What do you understand by dependency preservation?**

Given a relation R and a set of FDs F, dependency preservation states that the closure of the union of the projection of F on each decomposed relation Ri is equal to the closure of F. i.e.,

((P_{R1}(F)) U … U (P_{Rn}(F)))^{+} = F^{+}

^{ }if decomposition is not dependency preserving, then some dependency is lost in the decomposition.

*55. ***What is meant by Proactive, Retroactive and Simultaneous Update.**

*Proactive Update:*

* *The updates that are applied to database before it becomes effective in real world .

*Retroactive Update: *

* *The updates that are applied to database after it becomes effective in real world .

*Simulatneous Update:*

* *The updates that are applied to database at the same time when it becomes effective in real world .

*56. ***What are the different types of JOIN operations?**

*Equi Join: *This is the most common type of join which involves only equality comparisions. The disadvantage in this type of join is that there