The Splitting/Combining Rule

Recall that in “Functional Dependencies” we defined the FD: A1A2…An → B1B2..Bm to be a shorthand for the set of FD's:

Trivial Functional Dependencies

A FD A1A2 . . . An → B is said to be trivial if B is one of the A's. For instance, title year → title is a trivial FD. Every trivial FD holds in every relation, since it says that "two tuples that agree in all of A1,

Computing the Closure of Attributes

Before proceeding to other rules, we shall give a general principle from which all rules follow. Assume {A1, A2,. . . ,An} is a set of attributes and S is a set of FD's. The closure of {A1, A2, .

Closing Sets of Functional Dependencies

As we have seen, given a set of FD's, we can sometimes infer some other FD's, including both trivial and nontrivial FD's. We shall, in later sections, want to differentiate between given FD's that are stated initially for a relation and derived FD's that are inferred using one of the

Projecting Functional Dependencies

When we learn design of relation schemas, we shall also have need to answer the following question about FD's. Assume we have a relation R with some FD's F, and we "project" R by removing certain attributes from the schema. Consider S is the relation that results from R if we

Selection / Cartesian Product

The selection operator, applied to a relation R, creates a new relation with a subset of R's tuples. The tuples in the resulting relation are those that satisfy some condition C that involves the attributes of R. We denote this operation σc(R). The schema for the resulting relation is the

Natural Joins / Theta-Joins

More frequently than we want to take the product of two relations, we find a need to join them by pairing only those tuples that match in some way. The simplest kind of match is the natural join of two relations R and S, denoted R x S, in which we pair only those tuples from R

A Linear Notation for Algebraic Expressions

In Combining Operations to Form Queries we used trees to represent complicated expressions of relational algebra. Another option is to invent names for the temporary relations that correspond to the interior nodes of the tree and write a sequence of assignments that create a

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