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In graph theory, the trivial graph is a graph which has only 1 vertex and no edge. Database theory has a concept called functional dependency, written . The dependence is true if Y is a subset of X, so this type of dependence is called "trivial". All other dependences, which are less obvious, are called "nontrivial".
Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: X → Y is called trivial if Y is a subset of X. In other words, a dependency FD: X → Y means that the values of Y are determined by the values of X. Two tuples sharing the same values of X will necessarily have the same values of Y.
If one of the tables in the join has all the attributes of the table , the join dependency is called trivial. The join dependency plays an important role in the fifth normal form (5NF), also known as project-join normal form, because it can be proven that if a scheme is decomposed in tables to , the decomposition will be a lossless-join ...
A set of vectors is said to be affinely dependent if at least one of the vectors in the set can be defined as an affine combination of the others. Otherwise, the set is called affinely independent. Any affine combination is a linear combination; therefore every affinely dependent set is linearly dependent.
A trivial multivalued dependency X Y is one where either Y is a subset of X, or X and Y together form the whole set of attributes of the relation. A functional dependency is a special case of multivalued dependency. In a functional dependency X → Y, every x determines exactly one y, never more than one.
Rational dependence. 1 language. ... is the trivial solution in which every k i is zero. The real numbers form a vector space over the rational numbers, ...
A multivalued dependency is a special case of a join dependency, with only two sets of values involved, i.e. it is a binary join dependency. A multivalued dependency exists when there are at least three attributes (like X,Y and Z) in a relation and for a value of X there is a well defined set of values of Y and a well defined set of values of Z.
Every non-trivial functional dependency begins with a superkey (a stricter form of 3NF) — Every non-trivial multivalued dependency begins with a superkey — Every join dependency has a superkey component [8] — Every join dependency has only superkey components — Every constraint is a consequence of domain constraints and key constraints