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Candidate Key
A candidate key, or simply a key, of a relational database is a minimal superkey. In other words, it is any set of columns that have a unique combination of values in each row (which makes it a superkey), with the additional constraint that removing any column would possibly produce duplicate rows (which makes it a minimal superkey). Specific candidate keys are sometimes called primary keys, secondary keys or alternate keys. The columns in a candidate key are called prime attributes, and a column that does not occur in any candidate key is called a non-prime attribute. Every relation without NULL values will have at least one candidate key: Since there cannot be duplicate rows, the set of all columns is a superkey, and if that isn't minimal, some subset of that will be minimal. There is a functional dependency from the candidate key to all the attributes in the relation. The candidate keys of a relation are all the possible ways we can identify a row. As such, they are an impo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relation Schema
In database theory, a relation, as originally defined by E. F. Codd, is a set of tuples (d1, d2, ..., dn), where each element dj is a member of Dj, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation. Instead, each element is termed an attribute value. An attribute is a name paired with a domain (nowadays more commonly referred to as a type or data type). An attribute value is an attribute name paired with an element of that attribute's domain, and a tuple is a ''set'' of attribute values in which no two distinct elements have the same name. Thus, in some accounts, a tuple is described as a function, mapping names to values. A set of attributes in which no two distinct elements have the same name is called a heading. It follows from the above definitions that to every tuple there corresponds a unique heading, being the set of names from the tup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternate Key
In the relational model of databases, a primary key is a ''specific choice'' of a ''minimal'' set of attributes (columns) that uniquely specify a tuple (row) in a relation (table). Informally, a primary key is "which attributes identify a record," and in simple cases constitute a single attribute: a unique ID. More formally, a primary key is a choice of candidate key (a minimal superkey); any other candidate key is an alternate key. A primary key may consist of real-world observables, in which case it is called a '' natural key'', while an attribute created to function as a key and not used for identification outside the database is called a ''surrogate key''. For example, for a database of people (of a given nationality), time and location of birth could be a natural key. National identification number is another example of an attribute that may be used as a natural key. History Although mainly used today in the relational database context, the term "primary key" pre-dates the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses Logical connective, logical operators such as Logical conjunction, conjunction (''and'') denoted as ∧, Logical disjunction, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''The Laws of Thought, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Implicant
In Boolean logic, the term implicant has either a generic or a particular meaning. In the generic use, it refers to the hypothesis of an implication (implicant). In the particular use, a product term (i.e., a conjunction of literals) ''P'' is an implicant of a Boolean function ''F'', denoted P \le F, if ''P'' implies ''F'' (i.e., whenever ''P'' takes the value 1 so does ''F''). For instance, implicants of the function :f(x,y,z,w)=xy+yz+w include the terms xy, xyz, xyzw, w, as well as some others. Prime implicant A prime implicant of a function is an implicant (in the above particular sense) that cannot be covered by a more general, (more reduced, meaning with fewer literals) implicant. W. V. Quine defined a ''prime implicant'' to be an implicant that is minimal - that is, the removal of any literal from ''P'' results in a non-implicant for ''F''. Essential prime implicants (aka core prime implicants) are prime implicants that cover an output of the function that no com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superkey
In the relational data model a superkey is a set of attributes that uniquely identifies each tuple of a relation. Because superkey values are unique, tuples with the same superkey value must also have the same non-key attribute values. That is, non-key attributes are '' functionally dependent'' on the superkey. The set of all attributes is always a superkey (the ''trivial superkey''). Tuples in a relation are by definition unique, with duplicates removed after each operation, so the set of all attributes is always uniquely valued for every tuple. A '' candidate key'' (or ''minimal superkey'') is a superkey that can't be reduced to a simpler superkey by removing an attribute. For example, in an employee schema with attributes employeeID, name, job, and departmentID, if employeeID values are unique then employeeID combined with any or all of the other attributes can uniquely identify tuples in the table. Each combination, , , , and so on is a superkey. is a candidate key--no subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Database
A relational database is a (most commonly digital) database based on the relational model of data, as proposed by E. F. Codd in 1970. A system used to maintain relational databases is a relational database management system (RDBMS). Many relational database systems are equipped with the option of using the SQL (Structured Query Language) for querying and maintaining the database. History The term "relational database" was first defined by E. F. Codd at IBM in 1970. Codd introduced the term in his research paper "A Relational Model of Data for Large Shared Data Banks". In this paper and later papers, he defined what he meant by "relational". One well-known definition of what constitutes a relational database system is composed of Codd's 12 rules. However, no commercial implementations of the relational model conform to all of Codd's rules, so the term has gradually come to describe a broader class of database systems, which at a minimum: # Present the data to the user as relati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primary Key
In the relational model of databases, a primary key is a ''specific choice'' of a ''minimal'' set of attributes (Column (database), columns) that uniquely specify a tuple (Row (database), row) in a Relation (database), relation (Table (database), table). Informally, a primary key is "which attributes identify a record," and in simple cases constitute a single attribute: a unique ID. More formally, a primary key is a choice of candidate key (a minimal superkey); any other candidate key is an alternate key. A primary key may consist of real-world observables, in which case it is called a ''natural key'', while an attribute created to function as a key and not used for identification outside the database is called a ''surrogate key''. For example, for a database of people (of a given nationality), time and location of birth could be a natural key. National identification number is another example of an attribute that may be used as a natural key. History Although mainly used today in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Database Normalization
Database normalization or database normalisation (see spelling differences) is the process of structuring a relational database in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity. It was first proposed by British computer scientist Edgar F. Codd as part of his relational model. Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of ''synthesis'' (creating a new database design) or ''decomposition'' (improving an existing database design). Objectives A basic objective of the first normal form defined by Codd in 1970 was to permit data to be queried and manipulated using a "universal data sub-language" grounded in first-order logic. An example of such a language is SQL, though it is one that Codd regarded as seriou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Key
{{Unreferenced, date=October 2020 In database design, a composite key is a candidate key that consists of two or more attributes (table columns) that together uniquely identify an entity occurrence (table row). A compound key is a composite key for which each attribute that makes up the key is a foreign key in its own right. Advantages Composite keys have advantages similar to that of a natural key as it is often composed of multiple natural key attributes. Storage Composite keys use less disk space as compared to defining a surrogate key column, this is because the composite key already exists as attributes in the table and does not need to be defined in the table just for the purpose of unique identification. This simplifies the table and also saves space. Easier to implement and use Composite keys are easy to implement in a database schema as their component parts are already named items in the database. When they are also natural keys, they are often intuitive for real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Set
In mathematics, the power set (or powerset) of a set is the set of all subsets of , including the empty set and itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of is variously denoted as , , , \mathbb(S), or . The notation , meaning the set of all functions from S to a given set of two elements (e.g., ), is used because the powerset of can be identified with, equivalent to, or bijective to the set of all the functions from to the given two elements set. Any subset of is called a ''family of sets'' over . Example If is the set , then all the subsets of are * (also denoted \varnothing or \empty, the empty set or the null set) * * * * * * * and hence the power set of is . Properties If is a finite set with the cardinality (i.e., the number of all elements in the set is ), then the number of all the subsets of is . This fact as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superkey
In the relational data model a superkey is a set of attributes that uniquely identifies each tuple of a relation. Because superkey values are unique, tuples with the same superkey value must also have the same non-key attribute values. That is, non-key attributes are '' functionally dependent'' on the superkey. The set of all attributes is always a superkey (the ''trivial superkey''). Tuples in a relation are by definition unique, with duplicates removed after each operation, so the set of all attributes is always uniquely valued for every tuple. A '' candidate key'' (or ''minimal superkey'') is a superkey that can't be reduced to a simpler superkey by removing an attribute. For example, in an employee schema with attributes employeeID, name, job, and departmentID, if employeeID values are unique then employeeID combined with any or all of the other attributes can uniquely identify tuples in the table. Each combination, , , , and so on is a superkey. is a candidate key--no subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
