MULTIVALUED DEPENDENCIES. Ha Do. Functional Dependency. a. 4. b. Q. c. $. Domain (X). Range (Y). Recall that if X uniquely determines Y, then Y is functionally dependent on X.
You may recall math the terms Domain and Range. The domain is the set of all values possible of X and the range is the set of all possible values of Y.
The relation is a function because each of the elements of X maps exactly to one element of Y.Functional Dependency
Let R be a relation schema and let and . The multivalued dependency α ->> β holds on R if, in any legal relation r(R), for all pairs of tuples t1 and t2 in r such that t1[α] = t2[α], there exist tuples t3 and t4 in r such thatt1[α] = t2[α] = t3[α] = t4[α]t3[β] = t1[β]t3[R − β] = t2[R − β]t4[β] = t2[β]t4[R − β] = t1[R − β]
sue a p1 b2
Then these tuples must also be in the relation.
Tuples Implied by name->->phones
If we have tuples:
name addr phones beersLiked
sue a p1 b1
sue a p2 b2
Here is possible data satisfying these MVD’s:
name areaCode phone beersLiked manf
Sue 650 555-1111 Bud A.B.
Sue 650 555-1111 WickedAle Pete’s
Sue 415 555-9999 Bud A.B.
Sue 415 555-9999 WickedAle Pete’s
But we cannot swap area codes or phones by themselves.
That is, neither name->->areaCode nor name->->phone
holds for this relation.
The following also involve functional dependencies:
The split of relations is guaranteed to be lossless if the intersection of the attributes of the new tables is a key of at least one of them.
The join connects tuples depending on the attribute (values) in the intersection. If these values uniquely identify tuples in the other relation we do not lose information.