Question

Consider a relation R(A, B, C), which of the following statements is not true according to inference rules for functional dependencies?
1. If A → B and B → C, then A → C
2. If AB → C, then A → B and B → C
3. If A → B and A → C, then A → BC
4. If A → B, then AC → BC

Answer 1

Correct Answer - Option 2 : If AB → C, then A → B and B → C

• Armstrong's axioms are the basic inference rule. Armstrong's axioms are used to conclude functional dependencies on a relational database.
• Inference rules for functional dependencies are transitive, union, augmentation, reflexive, and decomposition

Option 1: True:

Transitive Rule

In the transitive rule, if A determines B and B determines C, then A must also determine C.

If A   →   B and B  →  C then A → C 

Option 3: True:

Union Rule

Union rule says, if A determines B and A determines C, then A must also determine B and C.

If A    →  B and A   →  C then A  →   BC 

Option 4: True:

Augmentation Rule

The augmentation is also called a partial dependency. In augmentation, if A determines C, then AC determines BC for any C.

If A → C then AC  →  BC  

Hence Option 2 is the correct Answer

Decomposition Rule

The decomposition rule is also known as the project rule. It is the reverse of union rule.

This rule says, if A determines B and C, then A determines B and A determines C separately.

If A   →   BC then  A  →   B and A  →  C