/    /  DBMS – Multivalued Dependencies  (MVD)

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 :

 

αβR-α-β
t1a1…..ai     ai+1…ajaj+1……an
t2a1…..ai    bi+1…bjbj+1……bn
t3a1…..ai    ai+1…ajbj+1……bn
t4a1…..ai    bi+1…bjaj+1……an

Example-1:

 

Stud-NameTele-NoCity
t1Riya1234567890Hyderabad
t2Riya5678901234Delhi
t3Riya1234567890Delhi
t4Riya5678901234Hyderabad

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)