List the ordered pairs in the relation R from A = 0,1, 2, 3, 4, B = 1, 2, 3, 4, 5, where Ris defined as (a, b) e Rif and only if a = 26 where a e A, be B Then R is O {(2, 1), (4, 2)} O {(2, 1), (4, 2), (0, 2)} O {(1,2), (2, 4), (0, 2)} O {(1,2), (4, 2)}

List the ordered pairs in the relation R from A = 0,1, 2, 3, 4, B = 1, 2, 3, 4, 5, where Ris defined as (a, b) e Rif and only if a = 26 where a e A, be B Then R is O {(2, 1), (4, 2)} O {(2, 1), (4, 2), (0, 2)} O {(1,2), (2, 4), (0, 2)} O {(1,2), (4, 2)}

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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Question 2 1 0 Consider the matrix 1 1 0 1 Write the relation S as a set of ordered pair. Row = 1 ,2 ,3 Column= a, b
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as
5 of 40 A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if every decomposed relation is in BCNF. Let R(A,B,C,D,E,F,G) be a relation with the FDs: F = {CD → G, DG → C, AD→ G, G –→A, AB → F}. Consider the decomposition of R into R1(C, D, G), R2(A, D, G), R3(A, B, F) and R4(C, E). Which of the following statements is TRUE about this decomposition? Select one: O Ris in BCNF but Not in 3NF. Ris in 3NF but Not in BCNF. R is Not in 3NF and Not in BCNF. O R is in 3NF and in BCNF.
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ZV• @ uo 9:19 1 Asiacell lln. docs.google.com a B = {1,2,3,4,5,6} Suppose R is relation on B×B with pair (a,b) such that a < b. R is represented as O { (2,5), (1,2), (3,4),(6,6)} O {(1,2),(2,1).(3,4),(5,6)} O {(0,1), (1,2),(3,4),(5,6),(2,3)} O {(1,2),(3,4), (5,6)} Construct a truth table for the statement. (p –→q)→(~p vq) *
Adjacency matrix. Given a relation relation (as a numpy.array, see example below) and number of nodes n, define a function adjacency to construct the adjacency matrix A (as a numpy.array).You can assume that n is a positive integer and treat relation as a list of directed edges. # Example from p112 of VMLSrelation = np.array([[1, 2], [1, 3], [2, 1], [2, 4], [3, 4], [4, 1]])n = 4 # Modify the function adjacency below with your answer for Q8def adjacency(relation, n): A = None ########################### ### YOUR CODE HERE ######## ## REMOVE THIS LINE-------- raise NotImplementedError() ## ------------------------ ########################### return A
B
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For non empty binary relation R={(a, a),(a, b),(b, a),(b, b),(c, c),(c, d),(d, c),(d, d)} on the set A={a, b, c, d, e}, which is the following is true? Symmetric а. Reflexive, Symmetric, Transitive Ob. Reflexive, Anti-Symmetric С. Transitive d. Reflexive, Transitive е. O f. Reflexive, Symmetric Anti-Symmetric, Transitive g. O h. Symmetric, Transitive Reflexive, Symmetric, Anti-Symmetric, Transitive i. Oj. Reflexive, Anti-Symmetric, Transitive Reflexive k.
a) Let A = {1, 2, 3, 4, 5, 6} and the relation R on A is defined by R = {(a, b)|a + b is odd; a, b e A} i. List all elements in R. ii. Find the matrix of the relation, MR iii. List in-degrees and out-degrees of each element in A. iv. Determine whether the relation R is transitive? Justify your answers.
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