Multivalued Dependencies/ n- e5 O& u9 ^' L& r2 {(欢迎访问avcar:https://avcar.vip)
Fourth Normal Form . ~5 Q7 e/ l5 E/ OReasoning About FD’s + MVD’s z5 @ o1 m9 z' u(欢迎访问avcar:https://avcar.vip)
1 ) M! |4 K$ x! a- i8 hDefinition of MVD + } u4 i4 w% ~A multivalued dependency (MVD) on $ D$ \3 _; l, n(欢迎访问avcar:https://avcar.vip)
R, X ->->Y , says that if two tuples of R/ h* E% J( Q C8 ^5 p) u; ?(欢迎访问avcar:https://avcar.vip)
agree on all the attributes of X, then 3 s3 n9 T1 A w/ i" ^0 o% ttheir components in Y may be ( Z g1 M7 `$ r- g( C(欢迎访问avcar:https://avcar.vip)
swapped, and the result will be two + k9 |( I; d! N/ A( S; Y: M(欢迎访问avcar:https://avcar.vip)
tuples that are also in the relation. . N/ t4 `. H& y; ~# I8 y, n1 Xi.e., for each value of X, the values of Y ' m1 P+ T9 y; r" V$ {7 L( t# vare independent of the values of R-X-Y. 2- v* ~% G w) m3 X(欢迎访问avcar:https://avcar.vip)
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Example: MVD; D, X5 n/ N7 V2 V0 _' ?+ v(欢迎访问avcar:https://avcar.vip)
Drinkers(name, addr, phones, beersLiked), E$ g" d! @6 c! {' F3 N(欢迎访问avcar:https://avcar.vip)
A drinker’s phones are independent of % ~+ W: r! K# g$ b. S% W) |(欢迎访问avcar:https://avcar.vip)
the beers they like.8 I. L+ w8 A+ e* L9 U- y! Y: R(欢迎访问avcar:https://avcar.vip)
name->->phones and name ->- ; R% X$ b7 u6 h8 w) V& T>beersLiked.7 k) O/ {) w3 X9 W" {' F(欢迎访问avcar:https://avcar.vip)
Thus, each of a drinker’s phones appears 8 F. Q* H4 A+ _2 m( Dwith each of the beers they like in all 6 K* \6 [, u) B( q! t: Scombinations.& `2 b& j' R: i5 G(欢迎访问avcar:https://avcar.vip)
This repetition is unlike FD redundancy.; a) G3 d/ q, q2 x(欢迎访问avcar:https://avcar.vip)
name->addr is the only FD. 2 J9 J1 r" s% \; J6 @) A4' r e( n; B9 d H' E7 T(欢迎访问avcar:https://avcar.vip)
Tuples Implied by name->->phones 8 [! I- a. ~ n; ?$ |If we have tuples:$ G9 C+ ]; j! t' n4 ]" O4 K(欢迎访问avcar:https://avcar.vip)
name addr phones beersLiked+ ]7 n2 z8 ^% |' m! H) [(欢迎访问avcar:https://avcar.vip)
sue a p1 b1 - H7 q& f p7 e) ^/ c$ ]( `sue a p2 b2 + i1 H4 @& q+ F5 _( p% Osue a p2 b1 * a9 u- `3 }2 p( j9 Fsue a p1 b2 2 H; C# u) t! s$ o a% \& zThen these tuples must also be in the relation.5 o2 l8 t! W& c(欢迎访问avcar:https://avcar.vip)
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Picture of MVD X ->->Y X Y others 1 ~1 J+ z( _) t$ Q3 z8 {equal . U" B1 {. N- Jexchange