Question

Suppose that we have the following legal instance of a relational schema R with attributes A, B, C and D Which of the following functional dependencies do not hold over R? Explain.

a) A→D
b) D→B
c) C→A
d) AB→C

Answer 1

To determine which of the given functional dependencies hold over the relational schema R, it is necessary to have the actual values in R. Each functional dependency holds if every unique combination of values in one set of columns corresponds to a unique combination of values in another column or set of columns. Examples and explanations are provided for each functional dependency.

Step-by-step explanation:

Let's analyze each functional dependency:

1. A→D: This functional dependency holds if every unique combination of values in column A corresponds to a unique combination of values in column D. For example, if A is the employee ID and D is the salary, then each employee has a unique salary. Otherwise, if there are multiple employees with the same salary, the functional dependency does not hold.
2. D→B: This functional dependency holds if every unique combination of values in column D corresponds to a unique combination of values in column B. For example, if D is the product ID and B is the product name, then each product has a unique name. If there are multiple products with the same ID but different names, the functional dependency does not hold.
3. C→A: This functional dependency holds if every unique combination of values in column C corresponds to a unique combination of values in column A. For example, if C is the country code and A is the country name, then each country has a unique name. If there are multiple countries with the same code but different names, the functional dependency does not hold.
4. AB→C: This functional dependency holds if every unique combination of values in columns A and B corresponds to a unique combination of values in column C. For example, if A is the customer ID, B is the order ID, and C is the order date, then each combination of customer ID and order ID has a unique order date. If there are multiple orders with the same customer ID and order ID but different order dates, the functional dependency does not hold.

Based on the information provided, I would need the actual values in the relational schema R to determine whether each functional dependency holds or not. Please provide the values in R to make an accurate determination.