written 7.9 years ago by | modified 2.3 years ago by |

a | b | C |
---|---|---|

A1 | B1 | C1 |

A1 | B1 | C2 |

A2 | B1 | C1 |

A2 | B1 | C3 |

Database Management System

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List all functional dependencies satisfied by the relation.

written 7.9 years ago by | modified 2.3 years ago by |

a | b | C |
---|---|---|

A1 | B1 | C1 |

A1 | B1 | C2 |

A2 | B1 | C1 |

A2 | B1 | C3 |

Database Management System

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written 7.9 years ago by |

**1. The functional dependencies satisfied by the relation are as follows:**

i. A → B

For the tuples t1(A1,B1,C1) and t2(A1,B1,C2), t1 (A) =t2(A)=A1 and t1(B)=t2(B)=B1. Thus, the functional dependency A→B is satisfied by the relation.

ii. C → B

For the tuples t1(A1,B1,C1) and t3(A2,B1,C2), t1 (C) =t3(C) =C1 and t1 (B)=t3(B)=B1. Thus, the functional dependency C→B is satisfied by the relation.

iii. The dependency AC→B can also be obtained.

**2. Following are the functional dependencies which are not satisfied.**

i. C does not functionally determine A because the tuples t1(A1,B1,C1) and t3(A2,B1,C1) have the same C but different A values.

ii. The same tuples also show B does not functionally determine A.

iii. A does not functionally determine C because the first two tuples t1(A1,B1,C1) and t2(A1,B1,C2)have the same A value and different C values.

iv. The same tuples also show B does not functionally determine C.

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