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Chapter 10: Problem 32

, Date_sold, Salesman#, Commission\%, Discount_amt) Assume that a car may be sold by multiple salesmen, and hence \(\\{\mathr… # Consider the following relation: CAR_SALE(Car#, Date_sold, Salesman#, Commission\%, Discount_amt) Assume that a car may be sold by multiple salesmen, and hence \)\\{\mathrm{CAR} \\#,\( SALESMAN is the primary key. Additional dependencies are Date_sold \)\rightarrow\( Discount amt and Salesman# \)\rightarrow\( Commission\% Based on the given primary key, is this relation in \)1 \mathrm{NF}, 2 \mathrm{NF}\(, or \)3 \mathrm{NF}$ ? Why or why not? How would you successively normalize it completely?

Short Answer

Expert verified
The initial relation CAR_SALE was in 1NF but not in 2NF due to the presence of partial dependencies. After further normalization, the revised relations SALE, SALESMAN, and CAR_SALE are in 3NF.

Step by step solution

01

Verify 1NF

To verify if the relation, CAR_SALE, is in its 1NF, we need to check whether it has any repeating groups. The relation has no repeating groups because each record is unique with respect to the primary key which is the combination of CAR# and SALESMAN#. Therefore, the relation is in 1NF.
02

Verify 2NF

To verify if the relation is in 2NF, we must ensure that there is no partial dependency i.e., no non-prime attribute is dependent on any proper subset of any candidate key. In this case, the dependencies Date_sold → Discount_amt and Salesman# → Commission\% both suggest that there are attributes (Discount_amt and Commission\%) that are dependent on a proper subset of the candidate key (CAR#, SALESMAN#). So, the given relation is not in 2NF.
03

Normalize to 2NF

The solution to normalize the relation to 2NF is to remove the partial dependencies. We create two new relations: SALE(Date_sold, Discount_amt) and SALESMAN(Salesman#, Commission\%). Now, the CAR_SALE relation will be (Car#, Date_sold, Salesman#).
04

Verify 3NF and Normalize if Necessary

To verify if the updated relations are in 3NF, we must ensure there's no transitive dependency. The relations SALE, SALESMAN, and CAR_SALE satisfy the conditions for 3NF as they do not have any non-prime attribute that is dependent on any non-candidate key attribute. Therefore, these relations are in 3NF.

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Most popular questions from this chapter

What does the term unnormalized relation refer to? How did the normal forms develop historically from first normal form up to Boyce-Codd normal form?

, Odate, Cust#, Total_amount) ORDER- ITEM(O#, I#, Qty_order… # Consider the following relations for an order-processing application database at \(\mathrm{ABC},\) Inc. ORDER (O#, Odate, Cust#, Total_amount) ORDER-ITEM(O#, I#, Qty_ordered, Total_price, Discount\%) Assume that each item has a different discount. The Total_PRICE refers to one item, OOATE is the date on which the order was placed, and the Total_AMOUNT is the amount of the order. If we apply a natural join on the relations ORDER-ITEM and ORDER in this database, what does the resulting relation schema look like? What will be its key? Show the FDs in this resulting relation. Is it in \(2 \mathrm{NF}\) ? Is it in \(3 \mathrm{NF}\) ? Why or why not? (State assumptions, if you make any.)

Why can we not infer a functional dependency automatically from a particular relation state?

Discuss insertion, deletion, and modification anomalies. Why are they considered bad? Illustrate with examples.

What role do Armstrong's inference rules- -the three inference rules IR 1 through IR3-play in the development of the theory of relational design?
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