4. A) Given the set A = {1,2,3,4} and relations R defined on set A as follows: R = {(1,1), (1,2), (2,1), (2,2), (3,3), (4,4)} i) Represent the relation R in a directed graph. ii) By explaining from the directed graph: Is the relation R reflexive? Symmetric? Asymmetric? Transitive? Equivalence? B) Solve the following recurrence relations using an appropriate method for each. i) Un = Un-1 + n² with U₁ = 3 ii) Un = 7Un-1 + 1 with U₁ = 1 iii) Un = 3Un-1 + 4Un-2 with Uo with Uo = 2 and U₁ = 3

4. A) Given the set A = {1,2,3,4} and relations R defined on set A as follows: R = {(1,1), (1,2), (2,1), (2,2), (3,3), (4,4)} i) Represent the relation R in a directed graph. ii) By explaining from the directed graph: Is the relation R reflexive? Symmetric? Asymmetric? Transitive? Equivalence? B) Solve the following recurrence relations using an appropriate method for each. i) Un = Un-1 + n² with U₁ = 3 ii) Un = 7Un-1 + 1 with U₁ = 1 iii) Un = 3Un-1 + 4Un-2 with Uo with Uo = 2 and U₁ = 3

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

Question 25 Please choose the right option wisely.
help me with the k-map and diagraph/graph of the following question
In conceptual graph, if a graph contains two duplicate relations, then one of them may be deleted, along with all its arcs. What this operator is called? a.Simplify b. Join c. Restrict d d. Copy
For A = {1,2,3,4,5}, the following are equivalence relations on A: R1 = {(1,1), (1,2), (2,1), (2,2,), (3,3), (3,4), (4,3), (4,4), (5,5) R2 = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,4), (4,5), (5,4), (5,5) a. Determine the (0,1) relation matrix for each of the equivalence relations above. b. If A = {1,2,3,4,5} and R is the equivalence relation on A that induces the partition A = {1,2} U {3,4} U (5}, what is R?
Let A ={1, 2, 3, ... , 10}, B = {2, 3, 6, 8}, and C = {3, 5, 4, 8, 2} Write the Venn diagram representation of the following sets. How many elements are there in A U B U C.
Let A be the towns {P, Q, R, S}. Let B be the one way street relation {(P, S), (Q, P), (R, P), (S, Q), (S, R)}. Find B^2 (pairs of towns that are connected by two streets). Find B3 (pairs of towns that are connected by three streets). You must use directed graph to find the answer.
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
in a graph G = (N,E,C), where N are nodes, E edges between nodes, and the weight of an edge e ∈ E is given by C(e), where C(e) > 1, for all e ∈ E. the heuristic h that counts the least amount of edges from an initial state to a goal state. now removing edges from the graph, while keeping the heuristic values unchanged. Is the heuristic still consistent?
Discrete Math
Please show step-by-step explanations and all of the reasoning. Thank you. Suppose G is a simple connected graph such that G is unicyclic. Prove that|V (G)| = |E(G)|.
For any graph G and H ⊆ G, we have G[V (G − E(H))] = G.True or False?
Question # 22: Suppose you have a function f (x) = – cos (æhd two nodes -5 and 0. 1. Find the interpolation polynomial of the given function and nodes using the Vandermonde matrix method. 2. Roughly hand-draw a comparison graph between f ()and the interpolating polynomial. 3. Compute the actual interpolation error at a = 0