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## 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 Solution: Visit for detailed answer here. 2. Let F = {A → B, A → C, BC → D}. Can A determine D uniquely? (a) Yes (b) No Solution: Visit for detailed answer here. 3. Let F = {AB → D, B → C, BC → D}. Can AC determine D uniquely? (a) Yes (b) No Solution: Visit for detailed answer here. 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 Solution: Visit for detailed answer here. 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} Solution: Visit for detailed answer here. 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} Solution: Visit for detailed answer here. 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)} Solution: Visit for detailed answer here. 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 Solution: Visit for detailed answer here. 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) Solution: Visit for detailed answer here. 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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