###### Database-Management-System

October 14, 2023###### Database-Management-System

October 14, 2023# Database-Management-System

Question 11 |

Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?

A cell in R holds a set instead of an atomic value. | |

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key.
| |

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key. | |

R has a nontrivial functional dependency X→A, where X is not a superkey and A is a prime attribute. |

Question 11 Explanation:

R(ABCD)

FDs:

AB → C

BC → A

(BD)

(ABD)

(CBD)

Candidate keys = {ABD, CBD}

• The relation R is in 3NF, as there are no transitive dependencies.

• The relation R is not in BCNF, because the left side of both the FD’s are not Super keys.

• In R, BC → A is a non-trivial FD and in which BC is not a Super key and A is a prime attribute.

FDs:

AB → C

BC → A

(BD)

^{+}= BD ✖(ABD)

^{+}= ABDC ✔(CBD)

^{+}= CBDA ✔Candidate keys = {ABD, CBD}

• The relation R is in 3NF, as there are no transitive dependencies.

• The relation R is not in BCNF, because the left side of both the FD’s are not Super keys.

• In R, BC → A is a non-trivial FD and in which BC is not a Super key and A is a prime attribute.

Correct Answer: D

Question 11 Explanation:

R(ABCD)

FDs:

AB → C

BC → A

(BD)

(ABD)

(CBD)

Candidate keys = {ABD, CBD}

• The relation R is in 3NF, as there are no transitive dependencies.

• The relation R is not in BCNF, because the left side of both the FD’s are not Super keys.

• In R, BC → A is a non-trivial FD and in which BC is not a Super key and A is a prime attribute.

FDs:

AB → C

BC → A

(BD)

^{+}= BD ✖(ABD)

^{+}= ABDC ✔(CBD)

^{+}= CBDA ✔Candidate keys = {ABD, CBD}

• The relation R is in 3NF, as there are no transitive dependencies.

• The relation R is not in BCNF, because the left side of both the FD’s are not Super keys.

• In R, BC → A is a non-trivial FD and in which BC is not a Super key and A is a prime attribute.

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