Normalize the table, find keys, find minimal cover - Solved exercise

Normalization Quiz - Find the keys, candidate keys of a relational table, find the minimal cover of set of functional dependencies, check whether two sets of FDs are equivalent

Normalization – Find keys, find minimal cover, check for equivalent FDs

 

1. Let F = {A → B, AB → E, BG → E, CD → I, E → C}. The closures, A+, (AE)+ and (ADE)+ will be ________.
(a) ABCE, ABDE, ABCDEI	(b) ABCE, ABCE, ABCDEI
(c) ABDE, ABCE, ABCDE	(d) ABCE, ABDE, ABCDI
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2. Let F = {A → B, A → C, BC → D}. Can A determine D uniquely?
(a) Yes	(b) No
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3. Let F = {AB → D, B → C, BC → D}. Can AC determine D uniquely?
(a) Yes	(b) No
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4. Let F1 = {A → C, AC → D, E → AD} and F2 = {A → CD, E → AH}. Are F1 and F2 are equivalent?
(a) Equivalent	(b) Not Equivalent
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5. Find the minimal cover of the set of functional dependencies given; {A → BC, B → C, AB → D}
(a) {A → C, B → C, AB → D}	(b) {A → C, B → C, B → D}
(c) {A → B, B → C, A → D}	(d) {A → BC, B → C, A → D}
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6. Find the minimal cover of the set of functional dependencies given; {A → C, AB → C, C → DI, CD → I, EC → AB, EI → C}
(a) {A → C, C → DI, C → I, E → A, EI → C}	(b) {A → C, C → D, C → I, EC → A, EC → B}
(c) {B → C, C → DI, D → I, E → AB, EI → C}	(d) {A → C, C → DI, CD → I, I → C}
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7. Consider a relation R with set of functional dependencies F as follows; {A → B, C → D, AC → E, D → F}. How many keys does R have and what are they?
(a) 1, {(AC)}	(b) 2, {(AC), (AD)}
(c) 3, {(AC), (BC), (ABD)}	(d) 2, {(AC), (ABD)}
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8. Consider a relation R(A, B, C, D, E) with FDs AB → C, CD → E, C → A, C → D, D → B. What are the keys of R?
(a) AB, AC, D	(b) AC, BD
(c) AC, AD	(d) AB, AD, C
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9. Consider a relation R(A, B, C, D, E) with FDs AB → C, C → A, C → BD, D → E. What are the keys of R? Decompose R into 3NF relations.
(a) {C}, R1(ABCD), R2(DE)	(b) {BD, AB}, R1(ABCD), R2(DE)
(c) {AB, C}, R1(ABCD), R2(DE)	(d) {BD}, R1(ABC), R2(CDE)
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10. Consider a relation with schema R(A, B, C, D) with functional dependencies, BC → A, AD → B, CD → B, AC → D. Find all the candidate keys of R.
(a) AC, BC, CD	(b) AC, BC
(c) AC, AD	(d) BC, CD, A
Solution: Visit for detailed answer here.

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