(p V r) - q ..t Step Proposition Justification 1 Hypothesis pVr Addition, 1 3 (p v r) -> q Hypothesis Modus Ponens, 2, 3 q->t Hypothesis Modus Ponens 4,5 2. 4,
Q: napsack problem) ven the weights and values of n items, and the capacity of a knapsack (W), find…
A: Dear Student, The main motive in knapsack problem is to maximize value given a weight limitation…
Q: 5. Check whether p →r is a valid conclusion from the following premises: p → q V ¬r,q →pAr.
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Q: 5. Check whether p → r is a valid conclusion from the following premises: p → q V ¬r, q → pAr.
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Q: #1. Given the following premises: (1) p (2) (pvr)→s (3) ~svq Prove q.
A: Solution is given below:-
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Q: 4. given y → u p → w prove [(p v q) ar] → (x V ¬y) using natural deduction
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- Question 1: In graph theory, a graph X is a "complement" of a graph F if which of the following is true? Select one: a. If X is isomorph to F, then X is a complement of F. b. If X has half of the vertices of F (or if F has half of the vertices of X) then X is a complement of F. c. If X has the same vertex set as F, and as its edges ONLY all possible edges NOT contained in F, then X is a complement of F. d. If X is NOT isomorph to F, then X is a complement of F. Question 2: Which statement is NOT true about Merge Sort Algorithm: Select one: a. Merge Sort time complexity for worst case scenarios is: O(n log n) b. Merge Sort is a quadratic sorting algorithm c. Merge Sort key disadvantage is space overhead as compared to Bubble Sort, Selection Sort and Insertion Sort. d. Merge Sort adopts recursive approachhello. I need help with this: determine whether the given pair of graphs is isomorphic. Exhibit an isomorphism or provide a rigorous argument that none exists. Make sure to show what u1 maps to what v, what u2 maps to what v, etc. ThanksGiveanexampleofarelational-algebraexpressionandaquery-processingstrategy in each of the following situations:a. MRU is preferable to LRU. b. LRU is preferable to MRU.
- y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Comment on the results from the graph and determine the value of the time when the waves are with the same phase and assemble constructively and the time when they are with phase of opposite and interfere destructively.Write a java program that takes a matrix representing an undirected graph (connectivity matrix) and finds the minimum spanning tree (using kruskal's or prim's algo.) of that graph and then print it graphically ( Graphical user interface should be used)Computer Science: Data Structures and Algorithm (C Programming) A strongly connected component (SCC) of a directed graph G(V,E) is a maximal set of vertices C⊆V suchthatforeverypairofverticesuandvinC,wehavebothu↝vandv↝u;that is, vertices u and v are reachable from each other.In the example graph given below, the sets of nodes a, b, e, c, d, f, g, and h each form a strongly connected component. Thus, the graph consists of 4 strongly connected components. (a) Breadth First Search (BFS) can be used in determining whether each node in a given directed graph is reachable by every other node. Give the pseudocode of an algorithm using BFS that determines whether a given directed graph is a single SCC. Also provide the explanation of your algorithm in plain English along with a runtime analysis. (b) Depth First Search (DFS) can be used to calculate strongly connected compo- nents in a graph. Give the pseudocode of an algorithm using DFS that calculates SCCs in a given directed graph. Also…
- 3. Assume a graph G = (V, E) represents a computer network where the vertices represent computers and the edges represent point-to-point network connections between the computers. Assume each edge (u, v) of G is associated with a real number f(u,v) between 0 and 1 which represents the probability that the corresponding network connection is faulty. Assume these probabilities are independent. a. Propose an algorithm that finds a path between two given vertices u and v with the smallest probability of being faulty (a path is faulty if at least one of its edges is faulty). b. Analyze the complexity of your algorithm.R-13.7 - Let G be a graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: Vertex: 1 2 3 4 5 6 7 8 Adjacent Vertices: (2, 3, 4) (1, 3, 4) (1, 2, 4) (1, 2, 3, 6) (6, 7, 8) (4, 5, 7) (5, 6, 8) (5, 7) Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table above. a. Draw G. b. Give the sequence of vertices of G visited using a DFS traversal starting at vertex 1. c. Give the sequence of vertices visited using a BFS traversal starting at vertex 1.2. For each graph representation, select the appropriate worst-case complexity for checking if two distinct vertices are connected: a. Adjacency Matrix: ________ b. Edge List: ________ c. Adjacency List: _________ Choices: O(V+E), O(E^2), O(V^2), O(E) Explain why.
- Algorithm 6.1 Spanning Tree Algorithm1: Input : G = (V, E) unweighted connected graph G2: Output : T = (V, ET ) spanning tree of G3: V ← {s}4: T ← Ø5: while V = V do continue until all vertices are visited6: select an arbitrary edge (u, v) such that u ∈ T and v ∈ G \ T7: V ← V ∪ {v}8: ET ← ET ∪ {(u, v)}9: end whilemake Python Implementation of given algorithmSuppose F, G and H are simple graphs. Suppose f is an isomorphism from F to G and g is an isomorphism from G to H. Which of the following functions h is an isomorphism from F to H?Determine whether or not the following statements are true or false. Provide evidence to support the validity of the correct claims and counterexamples to support the falsity of the false assertions.I Every bipartite graph has a planar form, just like every other graph.(2) Each bipartite has two chromatic numbers, one for each half of the bipartite.