Question

Given the table X: X(A,B,C,D,E,F,G,H) And the functional dependencies:

A→{C,H}
B→D
G→A
{E,F}→{G,B}
​a)In which normal form is this table?
b)If it is not already in 3NF, re-write it as a set of one or more tables that are in 3NF.

Answer 1

The table X is in 1NF because all attributes meet the requirement of having atomic values. It is not in 2NF or 3NF due to partial and transitive dependencies. To achieve 3NF, the table must be decomposed into four separate tables with appropriate primary and foreign keys.

Step-by-step explanation:

The evaluating the normal form of a given table X with attributes (A, B, C, D, E, F, G, H) based on provided functional dependencies. To determine the normal form, we follow the rules for 1NF (First Normal Form), 2NF (Second Normal Form), and 3NF (Third Normal Form).

a) The table X is in 1NF because the values in the table are atomic and each column contains values of a single data type. However, it is not in 2NF or 3NF because there are dependencies where a non-primary key attribute depends on a part of a composite primary key (if we assume a composite key includes A and E,F).

b) To convert this table to 3NF, we decompose it as follows:Table1 (A, C, H) with A as the primary key. Table2 (B, D) with B as the primary key. Table3 (G, A) with G as the primary key and A as a foreign key. Table4 (E, F, G, B) with E,F as the composite primary key and G, B as foreign keys. This restructuring ensures that each table is in 3NF, where every non-key attribute is non-transitively dependent on the primary key.