Q4.Given A={1,2 , 3} and B={a, b} provide 1 possible relation from A to Bi.e., ARB. Q5. Given A={1, 2, 3}, B={a, b, c} and a relation from A to Bi.e., ARB= {(1,a), (1,b), (2,b), (2,c), (3,a)}, represent this relation in a mapping format and matrix format,

Q4.Given A={1,2 , 3} and B={a, b} provide 1 possible relation from A to Bi.e., ARB. Q5. Given A={1, 2, 3}, B={a, b, c} and a relation from A to Bi.e., ARB= {(1,a), (1,b), (2,b), (2,c), (3,a)}, represent this relation in a mapping format and matrix format,

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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8 of 40 Let R(A, B, C, D, E, F) be a relation with FD's: {D → C, C → D, D – E, C → E, E → AD, AF → E, D → B}. Which of the following statements is correct? Select one: O R is not in 3NF but in BCNF. Ris not in 3NF and not in BCNF. O Ris in 3NF but not in BCNF. O R is in 3NF and in BCNF.
Consider the relation instance and functional dependencies below. Which of these FDs hold on the instance and which do not? A BC 2 4 АВ — С A → B A → C В > с АС — В ВС — А 3 4 В > А C → A C → B 1 3 5 2 4
Solve the following:
Let W(A, B) and Q(C,D) be two relation schemas. Let r₁ and r2 be the corresponding relation instances. B is a foreign key that refers to C in r2. Assuming that all tuples in r₁ and r2 satisfy referential integrity constraints, which of the following is ALWAYS TRUE? (А) Пв (г1) - Пс (rz) =Ø (B) IIc (₂)-118 (1₁) = 0 (С) Пв (г1 ) = Пс (12) (D) Пв (r1 ) - Пс (12) +Ø OB OD OA O C
23 of 40 Let R(A, B, C, D, E, F) be a relation with FD's: {D → CE, C → BDE, E → AD, AF → E, B → DF}. Which of the following statements is correct? Select one: O Ris in BCNF but not in 3NF. O Ris in 3NF but not in BCNF. O Ris not in 3NF and not in BCNF. O R is in 3NF and in BCNF.
For each of the following pairs of expressions, give instances of relations thatshow the expressions are not equivalent. ΠA(r − s) and ΠA(r) − ΠA(s).
Given relation R(u, y, c, d, e, f, w) where there are two keys: {y,c} and {w}. Given a set of functional dependencies F = {fd1: {y,c} -> {u,d,e,f,w}, fd2: u -> c, fd3: w -> {u,y,c,d,e,f}}. Is R in 3NF? Explain why.
Task 4: Consider the relation schema R(A, B, C, D, E) with the following FDs FD1: {A,B,C} → {D,E} FD2: {B,C,D} → {A,E} FD3: {C} → {D} a) Show that R is not in BCNF. Ans) X = {C} then X+ = {C, D} which is not R therefore X is not a superkey, so R is not in BCNF. b) Decompose R into a set of BCNF relations (describe the process step by step). Ans) FD3 violates BCNF. Decomposing R using FD3. R1(C,D) with FDs: FD3, CK: {C} R2(A,B,C,E) with new FD: {A,B,C}→ E (Decomposed from FD1), CK: {A,B,C} {BC}+ = {BC} - Not a candidate key {ABC}+ = {ABCDE} - A candidate key {BCD}+ = {ABCDE} - A candidate key Candidate Keys = {ABC}, {BCD} The result of the decomposition consists of R1 and R2 %3D %3D
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Solve the following:
Given the reation R (A, B, C, D , E), with functional dependencies: A, B -> C D, E -> C B -> D Could you explain why this is not functional dependency preserving? Also could you work out the BCNF for this?