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In functional dependency Armstrong inference rules refers to
- a)Reflexivity, Augmentation and Decomposition
- b)Transitivity, Augmentation and Reflexivity
- c)Augmentation, Transitivity, Reflexivity and Decomposition
- d)Reflexivity, Transitivity and Decomposition
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In functional dependency Armstrong inference rules refers toa)Reflexiv...
Armstrong inference rules refer to a set of inference rules used to infer all the functional dependencies on a relational database. It consists of the following axioms:
Axiom of Reflexivity:
This axiom states: if Y is a subset of X, then X determines Y
Axiom of Augmentation:
The axiom of augmentation, also known as a partial dependency,
states if X determines Y, then XZ determines YZ, for any Z
Axiom of Transitivity:
The axiom of transitivity says if X determines Y, and Y
determines Z, then X must also determine Z.
Axiom of Reflexivity:
This axiom states: if Y is a subset of X, then X determines Y
Axiom of Augmentation:
The axiom of augmentation, also known as a partial dependency,
states if X determines Y, then XZ determines YZ, for any Z
Axiom of Transitivity:
The axiom of transitivity says if X determines Y, and Y
determines Z, then X must also determine Z.
Most Upvoted Answer
In functional dependency Armstrong inference rules refers toa)Reflexiv...
Armstrong inference rules refer to a set of inference rules used to infer all the functional dependencies on a relational database. It consists of the following axioms:
Axiom of Reflexivity:
This axiom states: if Y is a subset of X, then X determines Y
Axiom of Augmentation:
The axiom of augmentation, also known as a partial dependency,
states if X determines Y, then XZ determines YZ, for any Z
Axiom of Transitivity:
The axiom of transitivity says if X determines Y, and Y
determines Z, then X must also determine Z.
Axiom of Reflexivity:
This axiom states: if Y is a subset of X, then X determines Y
Axiom of Augmentation:
The axiom of augmentation, also known as a partial dependency,
states if X determines Y, then XZ determines YZ, for any Z
Axiom of Transitivity:
The axiom of transitivity says if X determines Y, and Y
determines Z, then X must also determine Z.
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Community Answer
In functional dependency Armstrong inference rules refers toa)Reflexiv...
Armstrong's Inference Rules in Functional Dependency
Armstrong's inference rules are a set of rules used in functional dependency to infer new functional dependencies from given ones. These rules are essential in database design and normalization. There are three main rules in Armstrong's inference rules: Transitivity, Augmentation, and Reflexivity.
1. Transitivity
The transitivity rule states that if X → Y and Y → Z hold, then we can infer that X → Z also holds. In other words, if we have a functional dependency X → Y and another functional dependency Y → Z, we can combine them to derive the new functional dependency X → Z.
2. Augmentation
The augmentation rule states that if X → Y holds, then we can infer that XZ → YZ also holds. This means that if we have a functional dependency X → Y, we can append the same attribute Z to both sides of the dependency to derive a new functional dependency XZ → YZ.
3. Reflexivity
The reflexivity rule states that if X is a set of attributes, then X → X holds. This means that every set of attributes determines itself.
Explanation of the Correct Answer (Option B)
The correct answer is option B, which states that Armstrong's inference rules include Transitivity, Augmentation, and Reflexivity. This answer is correct because these three rules are indeed the fundamental rules in Armstrong's inference rules.
The option does not include Decomposition, which is not a part of Armstrong's inference rules. Decomposition is a separate concept used in functional dependency, but it is not included in the set of rules provided by Armstrong.
Therefore, the correct answer is option B, Transitivity, Augmentation, and Reflexivity.
Armstrong's inference rules are a set of rules used in functional dependency to infer new functional dependencies from given ones. These rules are essential in database design and normalization. There are three main rules in Armstrong's inference rules: Transitivity, Augmentation, and Reflexivity.
1. Transitivity
The transitivity rule states that if X → Y and Y → Z hold, then we can infer that X → Z also holds. In other words, if we have a functional dependency X → Y and another functional dependency Y → Z, we can combine them to derive the new functional dependency X → Z.
2. Augmentation
The augmentation rule states that if X → Y holds, then we can infer that XZ → YZ also holds. This means that if we have a functional dependency X → Y, we can append the same attribute Z to both sides of the dependency to derive a new functional dependency XZ → YZ.
3. Reflexivity
The reflexivity rule states that if X is a set of attributes, then X → X holds. This means that every set of attributes determines itself.
Explanation of the Correct Answer (Option B)
The correct answer is option B, which states that Armstrong's inference rules include Transitivity, Augmentation, and Reflexivity. This answer is correct because these three rules are indeed the fundamental rules in Armstrong's inference rules.
The option does not include Decomposition, which is not a part of Armstrong's inference rules. Decomposition is a separate concept used in functional dependency, but it is not included in the set of rules provided by Armstrong.
Therefore, the correct answer is option B, Transitivity, Augmentation, and Reflexivity.
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