## Define multivalued dependency and 4nf, Database Management System

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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.

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