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E.g. a call to a log() function may induce a transitive dependency to a library that manages the I/O of writing a message to a log file. Dependencies and transitive dependencies can be resolved at different times, depending on how the computer program is assembled and/or executed: e.g. a compiler can have a link phase where the dependencies are ...
To rephrase Zaniolo's definition more simply, the relation is in 3NF if and only if for every non-trivial functional dependency X → Y, X is a superkey or Y \ X consists of prime attributes. Zaniolo's definition gives a clear sense of the difference between 3NF and the more stringent Boyce–Codd normal form (BCNF).
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
This relation need not be transitive. The transitive extension of this relation can be defined by (A, C) ∈ R 1 if you can travel between towns A and C by using at most two roads. If a relation is transitive then its transitive extension is itself, that is, if R is a transitive relation then R 1 = R.
A depends on B and C; B depends on D. Given a set of objects and a transitive relation with (,) modeling a dependency "a depends on b" ("a needs b evaluated first"), the dependency graph is a graph = (,) with the transitive reduction of R.
Reflexive and transitive: The relation ≤ on N. Or any preorder; Symmetric and transitive: The relation R on N, defined as aRb ↔ ab ≠ 0. Or any partial equivalence relation; Reflexive and symmetric: The relation R on Z, defined as aRb ↔ "a − b is divisible by at least one of 2 or 3." Or any dependency relation.
Actress Susan Lucci spoke to Good Housekeeping about the All My Children at 55 reunion hosted by Andy Cohen, and whether she'd reprise her character Erica Kane.
The action is simply transitive (or sharply transitive, or regular) if it is both transitive and free. This means that given x, y ∈ X the element g in the definition of transitivity is unique. If X is acted upon simply transitively by a group G then it is called a principal homogeneous space for G or a G-torsor.