Question 2 Composite relations can be thought of as composite functions. If S is a relation from set A to B, and R from B to C, then composite relation Ro S passes an input acA first to S, then passes the return beB to R, and finally returns the output ceC, resulting in the set of pairs (acA, ceC). Relations R and S are shown below: • R= {(1,2), (2, 3), (2, 4), (3, 3), (4, 1)} • S = {(1,1), (1, 4), (2, 3), (2, 4), (3, 1), (4, 4)} Write the sets of pairs of composite relations (i) Ro R and (ii) Ro S.

Question 2 Composite relations can be thought of as composite functions. If S is a relation from set A to B, and R from B to C, then composite relation Ro S passes an input acA first to S, then passes the return beB to R, and finally returns the output ceC, resulting in the set of pairs (acA, ceC). Relations R and S are shown below: • R= {(1,2), (2, 3), (2, 4), (3, 3), (4, 1)} • S = {(1,1), (1, 4), (2, 3), (2, 4), (3, 1), (4, 4)} Write the sets of pairs of composite relations (i) Ro R and (ii) Ro S.

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

See similar textbooks

Similar questions

A relation, R, on non-empty set A is defined as a subset of A × A: R ⊆ A × A For example, let A = {1, 2, 3} then Cartesian product A × A = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}. A binary relation R ⊆ A × A Briefly explain the meaning of the relation, providing an example (and diagram): (i)) Discuss the real-life applications of binary relations
Show that the following decomposition of the schema R of Exercise 7.1 is not alossless decomposition:(A, B, C)(C, D, E).Hint: Give an example of a relation r(R) such that ΠA, B, C (r) ⋈ ΠC, D, E (r) ≠ r
Consider the relation schema R(A, B, C, D, E, F) and the set S = {AB->C, BC->AD, D->E, C->B) of functional dependencies. Assuming that R is decomposed into the relation schemas R1(A,B), R2(B,C), R3(A,B,D,E) and R4(E,F). Use the Chase test to show if this is a lossless decomposition.
Suppose R is a relation with attributes A1, A2, ..., An. As a function of n, tell how many superkeys R has, if The only keys are A1 and A2?
Consider a relation with schema R(A,B,C,D,E,G) and functional dependencies (FDs) C→D; B→A; D→E; E→G ) What is the closure of {B,C}? Show steps of your solution. Find 2 nontrivial FDs that can be inferred from the given FDs set. Explain how you found them. Propose one key for a given schema and FDs. Explain how you found it.
Consider a relation schema R(A, B, C, D, E, G) and a set of functional dependencies F = {A → C, AD → CE, B → ACD, C → B}. (a) Show the steps of computing a canonical cover for F. (b) Compute the closure of AG and then determine whether or not AG is a candidate key. (c) Determine whether or not (A, E, G) is in BCNF and justify your answer using the transitive closure of a set of attributes. If (A, E, G) is not in BCNF, find a BCNF decomposition of it. (d) Assume that (A, E, G) is decomposed into (A, G) and (E, G). Given the above functional dependencies, is this decomposition always lossless? If so, prove this. Otherwise, explain it using an example (i.e., a case of decomposing a table containg rows and columns into two tables). (e) Assume that R is decomposed into R1(A, B, C, D) and R2(A, E, G). Is this decomposition dependency preserving? Justify your answer.
The relation R defined on ℝ where aRb if and only if a< b is an equivalence relation. True or False
. A relation R on a set S, defined as x R y if and only if y R x. This is an example of?a) reflexive relationb) symmetric relationc) transitive relationd) invalid relation
Consider the relation R(A, B, C, D, E) and the set F = {AB → CE, E → AB, C → D}. What is the highest normal form of this relation? Explain your answer.
Given: Relation R = {(a,a), (a.b), (b,a). (b,b). (c,c)} and Set S = {a, b, c} Complete Relation R to be Transitive with Set S
Suppose that we have the following four tuples in a relation S with three attributes ABC: (1,2,3), (4,2,3), (5,3,3), (5,3,4). Which of the following functional (-->) and multivalued (-->>) dependencies can you infer does not hold over relation S? a) A-->Bb) A-->>Bc) BC-->Ad) BC-->>Ae) B->Cf) B-->>C
Suppose RR is a relation with attributes A1,A2,…,AnA1,A2,…,An. How many superkeys will RR have if a) The only candidate key is A1A1. b) The only candidate keys are A1A2A1A2 and A1A3A1A3.