2. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = { {x,y} {z,w,k,t}, z {x,y,w,k,t }, yt}. Is R in 2nd normal form? Justify your answer.
3. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = { fd1:{x,y} {z,w,k,t}, fd2: z {x,y,w,k,t }, fd3:k x}. Is R in 3rd normal form? Justify your answer.
4. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the following functional dependency: F = { fd1:{x,y} {z,w,k,t}, fd2: z {x,y,w,k,t }, fd3: w y}. Is R in BCNF? Justify your answer.
2. R (x,y, z, w, k, t).
Given FDs
{x,y} -> {z,w,k,t}
y->t
A Relation R is in second normal form if following conditions hold:
1.The relation R is in first normal form.
2.No non-prime attribute is dependent on proper subset of any candidate key. (Partial dependency)
Since there is a partial dependency, (ie. in y->t, y is a prime attribute.) , it violates 2NF.
*************************************************************************************************************
(3) Given fd1: {x,y} -> {z,w,k,t},
fd2: z -> {x,y,w,k,t },
fd3: k-> x
A Relation R is in third normal form if following conditions hold:
1.The relation R is in second normal form.
2.Every non-prime attribute of R is non-transitively dependent on every key of R.
Since there is no partial dependency, it is in 2NF and every non prime attributes ie. w, k and t are non transitively depend on the keys of R, the relation is in 3 NF.
4. Given fd1:{x,y} -> {z,w,k,t},
fd2: z -> {x,y,w,k,t },
fd3: w -> y
BCNF is a strict form of 3NF.
For a table to satisfy the Boyce-Codd Normal Form, it should satisfy the following two conditions:
Here xy and z are super keys but w is not a super key. so the relation is not in BCNF.
2. Given R(x,y, z, w, k, t). There are two keys: (x,y) and z. Given the...
Write the complete proof. Consider the relational schemas given below and the respective sets of functional dependencies valid in the schemas For each one of the relational schemas, determine the highest normal form, which is valid for a schema. Justify your answer If a schema is not in BCNF, then decompose it into a minimum number of schemas so that each one of them is in BCNF. Justify your answers. Justification must include the derivations of minimal keys from the...
Consider the following relation R, where {A, B} is its PK. Assume that R is in the first normal form (INF). R (A, B, C, D, E, F) Functional dependencies: FD1: BàC FD2: AàDE FD3: ABàF Why is this table not in 2NF? Specify which FDs make R violate 2NF. Normalize the data shown in this table to second normal form (2NF). Specify the primary and foreign key (if any) in each table of your 3NF relations. Normalize the data...
Consider a relation R(A,B,C,D,E) with the following functional dependencies: 8. AB C BCD CDE DEA (a) Specify all candidate keys for R. (b) Which of the given functional dependencies are Boyce-Codd Normal Form (BCNF) violations'? (c) Give a decomposition of R into BCNF based on the given functional dependencies. (d) Give a different decomposition of R into BCNF based on the given functional dependencies. (e) Give a decomposition of R into 3NF based on the given functional dependencies. Consider a...
Q3: Given a relational schema R = {A,B,C,D,E,F,G,H,1,J,K} and a set of functional dependencies F {A B C D E, E F G H I J,AI →K} and a key(R) = AI = 1. Is R in BCNF? If yes, justify your answer [5 points] 2. If no, explain why and decompose R for two levels only [10 points] 3. Check whether the decomposition in step 2 dependency preserved or not [5 points]
Language: SQL - Normalization and Functional Dependencies Part 4 Normalization and Functional Dependencies Consider the following relation R(A, B, C, D)and functional dependencies F that hold over this relation. F=D → C, A B,A-C Question 4.1 (3 Points) Determine all candidate keys of R Question 4.2 (4 Points) Compute the attribute cover of X-(C, B) according to F Question 43 (5 Points) Compute the canonical cover of F.Show each step of the generation according to the algorithm shown in class....
Q3: Given a relational schema ? = {?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?} and a set of functional dependencies ? = {? → ? ? ? ?, ? → ? ? ?, ? → ?, ? ? → ?} and a key(R) = AI 1. Is R in BCNF? If yes, justify your answer. 2. If no, explain why and decompose R for two levels only. 3. Check whether the decomposition in step 2 dependency...
Consider the following FD set on a relation E with six attributes: F, R, I, D, A, and Y. YI FI D A F D R DR A Its candidate keys are [(YF), (YD), (YA)} Tasks: 1. List prime attributes and non-prime attributes for the relation E. Justify your answer. 2. Classify each functional dependence for the relation E. Justify your answer. 3. Determine the normal form of the relation E. Justify your answer. Consider the following FD set on...
Exercise 4 Determine whether or not the following Σ11 and Σ12 are equivalent. Show and explain your answer R1= {A, B, C}, Σ11 = {A->B, A->C, C->A} and Σ12 = {A->B, AB->C, A->C, C->A} on R1, respectively. Exercise 5 Decompose the following into BCNF R = (A, B, C) F = {A → B, B → C} Exercise 6 George withdraws $100 from his account (T1) while Mary deposits$500 into George’s account (T2) in the following transaction process. Draw up...
The following logic function is given as a sum of minterms F(W,X,Y,Z) = ∑W,X,Y,Z(2,7,10,13,14) + d(5,6,15) a) Draw the K-map for the given function F. b) What is the minimized SOP equation? c) Give all input pairs in the form of WXYZ where a transition between them would create a timing hazard. d) Draw the timing diagram showing the hazard for one of the cases. Assume ALL gate delays are equal. e) Provide the expression of an equivalent logic function...