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1、……………………………………………………………最新资料推荐…………………………………………………Exｅｒcisｅ3．1．1Ａnｓwｅｒsfoｒthisｅxｅrcｉse mａyvａrybecａｕseofdifｆｅｒenｔinterｐｒetａtioｎs．Someposｓｉble FDs:ﻩSocial Sｅcurity ｎumberà nａmeﻩAｒeａ cｏdｅà stateﻩStreetaddresｓ,cｉｔy，sｔateà ziｐcodePossible keyｓ:｛SｏcｉalＳeｃuriｔynｕmｂer，
2、sｔrｅeｔaｄdress，ｃitｙ,ｓtａｔｅ, areａcode,phone nｕmbeｒ｝Neｅdｓtreetａddress, city,sｔaｔe touniｑｕｅly determｉｎeｌｏcaｔｉｏｎ.Apersoncould hａvemｕｌtｉpleａddreｓses。Thｅsame is trueforphones.These days,apeｒson coｕldhaｖeａ landlineanｄa cｅlｌuｌａｒpｈｏｎeEｘeｒcise3．1。2Answersfortｈisｅxｅｒcise
3、mａyvａｒybecauｓeof dｉfｆeｒeｎtｉｎterpretａtionsSｏmepossiｂｌe FDs:IDàx—ｐosition,y—ｐosｉtiｏn,z－posiｔｉonﻩＩＤàx-ｖelociｔy，y－velocity， z—veloｃityx—positioｎ,y-poｓition, z—positioｎàＩDPossiblekeys:｛ＩD}ﻩ{x—pｏｓitiｏn, y—ｐosition， z—ｐoｓｉtｉon}Theｒeasonwｈy thepｏsiｔionswouｌｄｂe akeｙ
4、is notwoｍoｌeculescanoccupyｔhesａmｅpoiｎt。Exercisｅ 3.1．3aＴheｓupｅrｋeyｓarｅａny sｕbｓｅtthatcontainsA１． Thus,ｔhｅre ａｒe2(n-1）such suｂsets, sincｅeａchofｔheｎ-1 ａttributesA２tｈroughAnmａy ｉｎdｅpendｅntｌｙbeｃｈosｅnｉｎ or out.Eｘercｉｓe3。1.3bThｅsｕperkeyｓ arｅ anysuｂseｔ thａtcoｎtａins A
5、1ｏrA2。 Thereare2(n-1） ｓｕchsubsetswhen ｃoｎsiｄeｒingＡ１andthen-１ attributesＡ2througｈAn． Therearｅ２(ｎ-2) sucｈｓubsｅｔswheｎconsiｄeriｎｇ A2 anｄthen-2attrｉbutesA３ throｕgｈAｎ。Wｅdo notｃｏuntA1ｉｎtｈｅsesuｂsｅtsbecａｕsetheｙaｒealreadｙ33/33……………………………………………………………最新资料推荐…………………………………
6、………………coｕnteｄinｔhｅ fｉrstｇｒｏupoｆｓｕbｓets.Thetotａl ｎumberｏfsubsetsiｓ2(n—1）+ ２（n-2）.Exeｒcｉsｅ3。1.3cＴhesｕperkeｙs aｒeany subsettｈａtcontａins {A1,Ａ２} or{A3,Ａ4}.Ｔhere ａre２（ｎ-２）ｓｕｃhsubｓetｓ whenconｓiderinｇ{A１,A２}anｄthｅn-2 ａttｒibutesA３ｔhroｕghAn.Theｒeare2（ｎ—２)– 2(n－4）such
7、subsetswhｅｎ consiｄｅring{Ａ３,A4｝ ａnｄ attｒiｂutesA5tｈｒoughAnalongwitｈthｅindｉvidualattribｕtes A1andＡ２。Wegｅtthe２(ｎ-4)terｍbecausｅwehａvetodiscarｄｔｈesuｂｓｅｔｓｔhaｔｃontaｉｎｔhekｅy｛Ａ1,A2｝toaｖoiddoｕblecｏｕｎting。Tｈetｏｔａl ｎuｍbｅr ofsuｂseｔs ｉs2(n－２) +2(n—２）–2(n—4）.Exercｉse3.1.3ｄT
8、ｈesuperkｅys aｒe anysubsｅtthaｔ coｎtains{A1,A2}or{A１，Ａ3}.Ｔherｅ ａre2(n-2)such ｓuｂsetｓ whenｃoｎｓidｅrinｇ｛Ａ1,Ａ2｝aｎdthen-2attｒiｂutｅｓA3throughAn。Theｒeare2（n-３)ｓuｃhsubsets whenｃｏnsiｄerinｇ｛Ａ1,A3}anｄ theｎ-３
