Multivalued Dependencies 5 `: T9 B% J8 L7 z! y _3 HFourth Normal Form ) K8 {; V. c3 x: K& A0 \- |/ X' u3 mReasoning About FD’s + MVD’s% _3 o' L3 B+ Z$ r# \" G(欢迎访问avcar:https://avcar.vip)
1 ' j8 ^& r9 |6 `' ^6 UDefinition of MVD 4 c4 \3 [# d3 ^2 p' ^% `A multivalued dependency (MVD) on 0 C- F- V% S* K9 T+ x" Z, cR, X ->->Y , says that if two tuples of R$ l2 d( ?2 M" Y# g8 w" N(欢迎访问avcar:https://avcar.vip)
agree on all the attributes of X, then 7 D$ Z( o1 i2 H( c+ n2 Ktheir components in Y may be 6 W [! S* ~( q8 C* \- [2 Y! Zswapped, and the result will be two - f! K3 Y" A' I(欢迎访问avcar:https://avcar.vip)
tuples that are also in the relation. ) U" m: ?8 K) N( L0 Ui.e., for each value of X, the values of Y2 B7 `, O5 y7 w( W4 T3 w(欢迎访问avcar:https://avcar.vip)
are independent of the values of R-X-Y. 2; p1 h" I. J/ s. R, Y7 j+ z(欢迎访问avcar:https://avcar.vip)
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Example: MVD% u; H. L1 o3 b3 b2 L: f; N J' ~8 T+ {(欢迎访问avcar:https://avcar.vip)
Drinkers(name, addr, phones, beersLiked) 8 ~* v9 O* }' T" K/ B/ k3 P& }$ C& rA drinker’s phones are independent of " C: Q4 ?) Q7 t1 z+ R" x' u(欢迎访问avcar:https://avcar.vip)
the beers they like. + @, |# I3 l( x$ h! `name->->phones and name ->- / ~" Z* C- F8 J/ L>beersLiked. 2 I; J$ b8 o# l) e( a$ JThus, each of a drinker’s phones appears 6 g' |7 M' Y0 K0 m$ {(欢迎访问avcar:https://avcar.vip)
with each of the beers they like in all 0 m o- ~' Z% j# ~8 k3 T(欢迎访问avcar:https://avcar.vip)
combinations. 2 c7 ?( _0 z/ B |This repetition is unlike FD redundancy. + M; U7 ^) V6 `; _3 u5 T9 iname->addr is the only FD. $ D5 P2 l2 r4 d9 h7 b6 I7 r3 i, @4& g. F7 X0 C+ m(欢迎访问avcar:https://avcar.vip)
Tuples Implied by name->->phones ) u+ C$ F& i5 F5 A; X2 lIf we have tuples: 3 | T. {( n9 C) \" @ tname addr phones beersLiked" J- |0 b+ Q5 `7 P9 D(欢迎访问avcar:https://avcar.vip)
sue a p1 b1 ( M! z$ k K9 Y! ]8 d3 A' k; nsue a p2 b2 % T) u- H( W# W" B3 Y0 o5 Dsue a p2 b10 C4 |: ^- a! s8 Z* H(欢迎访问avcar:https://avcar.vip)
sue a p1 b2! _$ z4 g% ]1 j+ c1 ](欢迎访问avcar:https://avcar.vip)
Then these tuples must also be in the relation.& T |% N3 U5 ]* C+ l: p: h/ W(欢迎访问avcar:https://avcar.vip)
5 ! Y9 C: Q$ K$ X+ p: D* l7 N0 h( I, dPicture of MVD X ->->Y X Y others & }4 d& D; |/ ?( Xequal % ?1 ]7 O' O. I4 i. G# ~9 Y7 rexchange