###### GATE 2022

October 16, 2023###### GATE 2022

October 16, 2023# GATE 2022

Question 14 |

In a relational data model, which one of the following statements is TRUE?

A relation with only two attributes is always in BCNF. | |

If all attributes of a relation are prime attributes, then the relation is in BCNF. | |

Every relation has at least one non-prime attribute. | |

BCNF decompositions preserve functional dependencies. |

Question 14 Explanation:

A relation with only two attributes will always be in BCNF.

Example:

R(A, B).

Two functional dependencies possible for the relation: (1) A->B and (2) B->A

If there is no functional dependency, we can assume trivial functional dependencies like AB->A and AB->B.

In all cases, functional dependencies like A->B, A must be a key.

So they all will be in BCNF irrespective of the functional depencies set.

Example:

R(A, B).

Two functional dependencies possible for the relation: (1) A->B and (2) B->A

If there is no functional dependency, we can assume trivial functional dependencies like AB->A and AB->B.

In all cases, functional dependencies like A->B, A must be a key.

So they all will be in BCNF irrespective of the functional depencies set.

Correct Answer: A

Question 14 Explanation:

A relation with only two attributes will always be in BCNF.

Example:

R(A, B).

Two functional dependencies possible for the relation: (1) A->B and (2) B->A

If there is no functional dependency, we can assume trivial functional dependencies like AB->A and AB->B.

In all cases, functional dependencies like A->B, A must be a key.

So they all will be in BCNF irrespective of the functional depencies set.

Example:

R(A, B).

Two functional dependencies possible for the relation: (1) A->B and (2) B->A

If there is no functional dependency, we can assume trivial functional dependencies like AB->A and AB->B.

In all cases, functional dependencies like A->B, A must be a key.

So they all will be in BCNF irrespective of the functional depencies set.

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