Define multivalued dependency and 4NF.

 Ans:  Multivalued Dependency - Assume R be a relation schema and let α ⊆ R and β ⊆ R. The multivalued dependency 

α →→β 

 holds on R if, in any type of legal relation r(R), for all pairs of tuples t₁ and t₂ in r like that 

t₁[α] = t₂[α], there exist tuples t₃ and t₄ in r like

t₁[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]

 Fourth Normal Form (4 NF) - A relation schema R is in 4NF regarding to a set D of functional and multivalued dependencies if, for all multivalued dependencies in D⁺ of the

form α →→β, in which α ⊆ R and β ⊆ R, at least one of the subsequent holds:

• α→→β is a trivial multivalued dependency,
• α is a superkey for schema R.