Boyce-Codd normal formWe have the attributes: {A, B, C, D, E}.Consider the following functional dependenciesC -> A, ED -> AA, B -> C, EE -> AC -> BThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):C -> BE -> AD -> AA, B -> EC -> AA, B -> CWe have also computed the minimal keys for you:{C, D}{B, D}Apply the synthesis algorithm to derive a Boyce-Codd normal form for the relation R(A, B, C, D, E).Write your answer as followsWrite one relation/table per line, for example, like:Relation1(A,B)Relation2(B,C,D)
Question
Boyce-Codd normal formWe have the attributes: {A, B, C, D, E}.Consider the following functional dependenciesC -> A, ED -> AA, B -> C, EE -> AC -> BThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):C -> BE -> AD -> AA, B -> EC -> AA, B -> CWe have also computed the minimal keys for you:{C, D}{B, D}Apply the synthesis algorithm to derive a Boyce-Codd normal form for the relation R(A, B, C, D, E).Write your answer as followsWrite one relation/table per line, for example, like:Relation1(A,B)Relation2(B,C,D)
Solution
To derive a Boyce-Codd normal form for the relation R(A, B, C, D, E), we apply the synthesis algorithm. The synthesis algorithm involves creating a new relation for each functional dependency in the canonical cover.
Here are the relations in Boyce-Codd Normal Form (BCNF):
Relation1(C, B) Relation2(E, A) Relation3(D, A) Relation4(A, B, E) Relation5(A, B, C)
Please note that the relations may vary based on the interpretation of the functional dependencies. The key point is that each relation should satisfy the conditions of BCNF, i.e., for any dependency A -> B, A should be a superkey.
Similar Questions
Third normal formWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesC, D, F -> GG -> DA -> GA, D -> BA, D -> CE -> C, DA, E -> C, GE -> GThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):G -> DC, D, F -> GA -> BA -> GE -> CE -> GA -> CWe have also computed the minimal keys for you:{A, E, F}Apply the synthesis algorithm to derive a third normal form for the relation R(A, B, C, D, E, F, G).Write your answer as followsWrite one relation/table per line, for example, like:Relation1(A,B)Relation2(B,C,D)
1. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesA, C, F -> D, EA -> CA, C, F -> B, EF -> A, BA, C -> E, F, GA, F, G -> C, DB, C -> DB -> AThe minimal keys are:{B}{F}{A}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form2. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesF -> E, GA, G -> C, D, EA, B -> FD -> F, GB, E, F -> D, GA, D, E -> B, FB, D, F -> A, EF, G -> B, D, EThe minimal keys are:{D}{F}{A, B}{A, G}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form3. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesB, C, D -> E, GB -> A, ED, E -> CA, C -> B, D, EB -> C, DD, F, G -> AG -> BB, C -> FThe minimal keys are:{B}{G}{A, C}{A, D, E}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form4. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesA, F, G -> CC, F -> GB -> C, FA, D, E -> CE, F, G -> B, CA, B, F -> D, E, GB, C -> A, DA, C, F -> GThe minimal keys are:{B}{C, E, F}{E, F, G}{A, D, E, F}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form5. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesD -> BF -> AB, C, D -> E, FA -> GE, F -> CA, D -> E, FE, F -> GC, F -> A, EThe minimal keys are:{D, F}{C, D}{A, D}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form6. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesC -> EE -> D, GD -> FF -> B, GF -> C, D, EG -> FC -> FC, G -> EThe minimal keys are:{A, E}{A, C}{A, F}{A, G}{A, D}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form
We have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesB, E -> C, D, FA, G -> B, CA, F -> B, DF, G -> ED, E -> A, B, GD, E -> A, BThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):B, E -> DD, E -> AA, F -> DA, F -> BA, G -> BB, E -> FF, G -> EA, G -> CD, E -> GApply the synthesis algorithm to derive a Boyce-Codd normal form for the relation R(A, B, C, D, E, F, G).Write your answer as followsFunctional dependencies: write one dependency per line, for exampleA,B -> CB,C,D -> A,FSplitting steps: write one split per line, for examplespliting R(A,B,C,D) into S(A,B,C) and T(A,D) -- the relation names are not importantspliting (A,B,C) into (A,B) and (A,C) -- and can even be omitted...
Which of the following normal forms is achieved when all non-key attributes are fully functionally dependent on the primary key?Question 11Answera.Second Normal Form (2NF)b.Boyce-Codd Normal Form (BCNF)c.First Normal Form (1NF)d.Third Normal Form (3NF)
Which normalization form eliminates transitive dependencies?Review LaterFirst Normal Form (1NF)Second Normal Form (2NF)Third Normal Form (3NF)Boyce-Codd Normal Form (BCNF)
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