Multivalued Dependencies  (MVD)

Definition :

Let  r( R) be a relation, and Let  α ⊆ R  and  β ⊆ R.

The Multivalued Dependency

                                                α →→ β

holds on R, if any legal relation r(R), for all pairs of tuples t1 and t2 in r such that  t1[α] = t2[α], there exists tuples t3 and t4 in r such that :            

  t1[α] = t2[α] = t3[α] = t4[α]   ………..(1)

t3[β] = t1[β]      …………………………….(2)

t3[R – β] = t2[R – β]     ………………….(3)

t4[β] = t2[β]      …………………………….(4)

t4[R – β] = t1[R – β]     ………………….(5)

Tabular Representation of  α àà β :

Example-1:

Note : 

1. a)  Here, MVD  α →⟶ β  is said to be trivial, if and only if

                                Β ⊆ α     or    α U β  = R.          

1. b) The following rules hold good for MVD.
2. i) Every FD is MVD.
3. ii)  If  α →→  β,  then  α →→ R – α – β

Reference Link

Multivalued Dependencies  (MVD)