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Which of the following statements about normal forms is false?
- a)BCNF is stricter than 3NF
- b)Lossless, dependency preserving decomposition into 3NF is always possible
- c)Lossless, dependency preserving decomposition into BCNF is always possible
- d)Any relation with two attribute is BCNF
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which of the following statements about normal forms is false?a)BCNF i...
Lossless, dependency preserving decomposition into BCNF is always possible,
Lossless, dependency preserving decomposition into BCNF is always not possible. All other statements are correct.
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Which of the following statements about normal forms is false?a)BCNF i...
Explanation:
To understand this question, we need to know the definitions of different normal forms.
1. First Normal Form (1NF): A relation is in 1NF if and only if all the domains of the attributes contain atomic values only.
2. Second Normal Form (2NF): A relation is in 2NF if it is in 1NF and every non-key attribute is fully functionally dependent on the primary key.
3. Third Normal Form (3NF): A relation is in 3NF if it is in 2NF and no non-key attribute is transitively dependent on the primary key.
4. Boyce-Codd Normal Form (BCNF): A relation is in BCNF if and only if every determinant is a candidate key.
Now let's go through each statement given in the question:
a) BCNF is stricter than 3NF: This statement is true. BCNF is stricter than 3NF because in BCNF, every determinant must be a candidate key, whereas in 3NF, some determinants can be non-prime attributes.
b) Lossless, dependency preserving decomposition into 3NF is always possible: This statement is true. It is always possible to decompose a relation into 3NF without losing any dependencies and without introducing any spurious tuples.
c) Lossless, dependency preserving decomposition into BCNF is always possible: This statement is false. It is not always possible to decompose a relation into BCNF without losing dependencies. In some cases, decomposition into BCNF will result in the loss of some functional dependencies.
d) Any relation with two attributes is BCNF: This statement is true. A relation with only two attributes will always be in BCNF because every determinant will be a candidate key.
In summary, option C is the false statement because it is not always possible to decompose a relation into BCNF without losing dependencies.
To understand this question, we need to know the definitions of different normal forms.
1. First Normal Form (1NF): A relation is in 1NF if and only if all the domains of the attributes contain atomic values only.
2. Second Normal Form (2NF): A relation is in 2NF if it is in 1NF and every non-key attribute is fully functionally dependent on the primary key.
3. Third Normal Form (3NF): A relation is in 3NF if it is in 2NF and no non-key attribute is transitively dependent on the primary key.
4. Boyce-Codd Normal Form (BCNF): A relation is in BCNF if and only if every determinant is a candidate key.
Now let's go through each statement given in the question:
a) BCNF is stricter than 3NF: This statement is true. BCNF is stricter than 3NF because in BCNF, every determinant must be a candidate key, whereas in 3NF, some determinants can be non-prime attributes.
b) Lossless, dependency preserving decomposition into 3NF is always possible: This statement is true. It is always possible to decompose a relation into 3NF without losing any dependencies and without introducing any spurious tuples.
c) Lossless, dependency preserving decomposition into BCNF is always possible: This statement is false. It is not always possible to decompose a relation into BCNF without losing dependencies. In some cases, decomposition into BCNF will result in the loss of some functional dependencies.
d) Any relation with two attributes is BCNF: This statement is true. A relation with only two attributes will always be in BCNF because every determinant will be a candidate key.
In summary, option C is the false statement because it is not always possible to decompose a relation into BCNF without losing dependencies.
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Which of the following statements about normal forms is false?a)BCNF is stricter than 3NFb)Lossless, dependency preserving decomposition into 3NF is always possiblec)Lossless, dependency preserving decomposition into BCNF is always possibled)Any relation with two attribute is BCNFCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which of the following statements about normal forms is false?a)BCNF is stricter than 3NFb)Lossless, dependency preserving decomposition into 3NF is always possiblec)Lossless, dependency preserving decomposition into BCNF is always possibled)Any relation with two attribute is BCNFCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements about normal forms is false?a)BCNF is stricter than 3NFb)Lossless, dependency preserving decomposition into 3NF is always possiblec)Lossless, dependency preserving decomposition into BCNF is always possibled)Any relation with two attribute is BCNFCorrect answer is option 'C'. Can you explain this answer?.
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