Question

Consider the following relation R, with key and functional dependencies shown below. i. What Normal form is R in right now? Why is this the case? ii. What actions would you take to normalize R to the next higher normal form? (Describe the steps) iii. Follow the steps you described in the prior question to normalize R to the next higher form. Be sure to show all of the steps. iv. Once you have normalized R, what normal forms are each the two ñew relations in? Why? v. If any of the remaining relations are not in 3NF, normalize them to 3NF. Be sure to show all of your work R(x1​,x2​,x3​,x4​,x5​,x6​,x7​,x3​) Key: x1​,x2​,x3​ FD1: x1​,x2​,x3​→x5​,x6​ FD2: x2​→x4​,xB​ FD3: x4​→x7​.

Answer 1

The given relation R is currently in the First Normal Form (1NF) because it contains atomic values in each attribute. To normalize R to the next higher normal form, we need to remove any functional dependencies that violate the higher normal form rules. The normalized relations would be R1(x1, x2, x3, x5, x6) and R2(x2, x4, x7), both in the Third Normal Form (3NF).

Step-by-step explanation:

The given relation R is currently in the First Normal Form (1NF) because it contains atomic values in each attribute. However, it is not in a higher normal form.

To normalize R to the next higher normal form, we need to remove any functional dependencies that violate the higher normal form rules. We can start by identifying the candidate keys of R, which are {x1, x2, x3} based on the given key dependency. Then, we check for dependencies involving these candidate keys and eliminate any partial dependencies and transitive dependencies.

Normalization to the next higher form would involve decomposing R into two new relations based on the functional dependencies. The first new relation would be R1(x1, x2, x3, x5, x6) and the second new relation would be R2(x2, x4, x7). Both of these new relations would be in the Third Normal Form (3NF) because they would not have any non-prime attributes functionally dependent on other non-prime attributes.