Ãîëîâíà

вØÅÍÍß 22

Consider R = {A, B, C, D, E} with a set of FDs F = {AB-> DE, C-> E, D-> C, E-> A}

And we wish to project those FDs onto relation S = {A, B, C}

Give the FDs that hold in S

Hint:

We need to compute the closure of all the subsets of {A, B, C}, except the empty set and ABC.

Then, we ignore the FD's that are trivial and those that have D or E on the RHS

гøåííÿ

Calculating F + for a Sub-Relations

R = {A, B, C, D, E}

F = {AB-> DE, C-> E, D-> C, E-> A}

S = {A, B, C}

A + = A

B + = B

C + = CEA [C-> E, E-> A]

AB + = ABDEC [AB-> DE, D-> C]

AC + = ACE [C-> E]

BC + = BCEAD [C-> E, E-> A, AB-> DE]

We ignore D and E.

So, the FDs that hold in S are:

{C-> A, AB-> C, BC-> A}

(Note: BC-> A can be ignored because it follows logically from C-> A)

Ðîçãëÿíüòå R = {A, B, C, D, E} ç ðÿäîì FDs F = {AB-> DE, C-> E, D-> C, E-> A}

² ìè õî÷åìî ñïðîåêòóâàòè ò³ FDs íà ñòàâëåííÿ S = {A, B, C}

Äàéòå FDs, ÿê³ òðèìàþòüñÿ â S

íàòÿê:

Ìè ïîâèíí³ îá÷èñëèòè çàêðèòòÿ âñ³õ ï³äìíîæèí {A, B, C}, êð³ì ïîðîæíüîãî íàáîðó ³ ABC.

Ïîò³ì ìè ³ãíîðóºìî FD's, ÿê³ òðèâ³àëüí³ ³ ò³, ó ÿêèõ º D àáî E íà RHS

гøåííÿ

Îá÷èñëåííÿ F + äëÿ ïîäîòíîøåí³ÿ

R = {A, B, C, D, E}

F = {AB-> DE, C-> E, D-> C, E-> A}

S = {A, B, C}

A + = A

B + = B

C + = CEA [C-> E, E-> A]

AB + = ABDEC [AB-> DE, D-> C]

AC + = ACE [C-> E]

BC + = BCEAD [C-> E, E-> A, AB-> DE]

Ìè ³ãíîðóºìî D ³ E.

Òàê, FDs, ÿê³ òðèìàþòüñÿ â S:

{C-> A, AB-> C, BC-> A}

(Ïðèì³òêà: BC-> A ìîæå áóòè ïðî³ãíîðîâàíèé, òîìó ùî â³í ñë³ä ëîã³÷íî â³ä C-> A)

ÂÀвÀÍÒ 23 (ÐÊ 1 / Ñåìåñòð 1)

Çíàéä³òü íåïðèâîäèìîãî ïîêðèòòÿ áåçë³÷³ ôóíêö³îíàëüíèõ çàëåæíîñòåé S = {AB-> D, B-> C, AE-> B, A-> D, D-> EF}, çàäàíèõ äëÿ çì³ííî¿-â³äíîñèíè R (A, B, C, D, E, F).

 Ð²ØÅÍÍß 20 |  Ð²ØÅÍÍß 23


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