Consider a relation R(A, B, C), which of the following statements is not true…
2025
Consider a relation R(A, B, C), which of the following statements is not true according to inference rules for functional dependencies?
- A.
If A → B and B → C, then A → C
- B.
If AB → C, then A → B and B → C
- C.
If A → B and A → C, then A → BC
- D.
If A → B, then AC → BC
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Correct answer: B
Solution
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
Additional Information
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