涉及空集的功能依赖性 [英] functional dependencies involving the empty set

问题描述

我正在尝试掌握FD的空集的概念。假设我有

I am trying to grasp the concept of the empty set with FDs. Say i have

R(A,B,C,D)

A-> E
B-> C
B-> D

其中E是空集，据我了解，这是一个微不足道的FD，因为您

where E is the empty set, from what I understand, this is a trivial FD, since you are learn nothing new from having A. But when you have

E-> A
B-> C
B-> D

这到底是什么意思？仅仅是什么都没有暗示A，因此A在定义的域内可以具有任何想要的值，还是A必须是NULL值？

what does this mean exactly? Is it simply "Nothing implies A", so A can have any value it wants within the defined domain or is it A must be a NULL value?

推荐答案

空集通常写为∅或{}。

The empty set is usually written as ∅ or {}.

• A-> {}很简单（因为{}是A的子集）。


• {}-> A并非无关紧要。（除非A是{}，因为{}是每个集合的子集，因此是

• A->{} is trivial. (because {} is a subset of A).
• {}->A is not trivial. (except if A is {}, since {} is the subset of every set, and so a subset of {} as well).

{}-> A表示A的值无需其他任何值即可确定。单词R的每个元组中A的值都必须相同。这与说A没有行列式或A为空相同。如果没有A的行列式，那么A将不受约束，并且在不同的元组中可以具有不同的值。

{}->A means the value of A can be determined without using any other value, in other words the value of A must be the same for every tuple in R. This is not the same as saying that A has no determinants or that A is null. If there were no determinants for A then A would be unconstrained and could have different values in different tuples.

对空集的依赖关系的一个示例可能是Sex属性在定义男士俱乐部会员资格的成员关系中：{}->性别。

An example of a dependency on the empty set might be the Sex attribute in a Members relation that defines the membership of a men-only club: {}->Sex.

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