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Dependencies
functional dependency
Attribute B of relation R is functionally dependent on attribute A if any value of attribute A corresponds to no more than one value b of attribute BA → B
X and Y are sub-sets of set of attributes of relation R
X ⊂ { A1...An}
Y ⊂ { A1...An}
Subset of attributes Y is fully functional dependent on
subset of attributes X . If it is not possible,
for relation R to contain two rows with
identical component that is consistent for all
from a set of attributes X and at the same time at
least one component is not in the
attributes from a set Y
X → Y
and also doesn't exist:
X' ⊂ X such that X' ⊂ Y
Funcional dependency - transitiveness
X , Y and Z are three disjoint subsets of attributes of given relation.Z is transitive functional dependent on X, if Z
is functional dependent on X but X isn't dependent on Y and
Y depends on Z.
Multi-valued dependency
Y is a subset of attributes wielowartościowo functionally dependent on X in the subset schema R, if for any relation r in schema R and for any pair of rows t1 and t2 from relationships r exist such pair of rows given below:s1[X]=s2[X]=t1[X]=t2[X] and
s1[Y]= t1[Y] and s1[R-X-Y]=t2[R-X-Y] and
s2 [Y]= t2[Y] i s2
[R-X-Y]=t1[R-X-Y]
| row | surname | name | course name |
|---|---|---|---|
| t1 | Burta | Anna | pedicure |
| t2 | Burta | Jan | swimming |
| s1 | Burta | Anna | swimming |
| s2 | Burta | Jan | pedicure |
| Balon | Albert | swimming | |
| Balon | Albert | pedicure |
t1[X]=t2[X]=s1[X]=s2[X]=(Burta)
s1[Y]= t1[Y]=(Anna) and
s1[R-X-Y]=t2[R-X-Y]=(swimming) and
s2 [Y]= t2[Y]=(Jan) and
s2
[R-X-Y]=t1[R-X-Y]=(pedicure)
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