Long chain of friends: You are given a list of people, and statements of the form “x knows y”. You are asked to find, is there a chain of k distinct people, such as x1 knows x2, x2 knows x3, and xk-1 knows xk. Prove that this problem is NP-complete by using one of the known NP-complete problems (CLIQUE, 3-SAT, Hamiltonian Path, Hamiltonian Cycle, Independent Set, etc.)

Q: We have been working extensively with the predicate "eventually greater than" defined on pairs of…

A: Given predicate is, "eventually greater than" which is defined on pairs of functions f and g. f(x)…

Q: For f(a, b) = (a | b) | b (a) Simplify f(a, b). (b) Find DNF for f(a, b). (c) Is f(a, b)…

A: (a) f(a, b) = (a | b) | b can be simplified as follows: f(a, b) = (a | b) | b = b | b (since a | b =…

Q: f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).

A: Proof: given: f:R---->R g:R----->R f(x) is O(g(x)) so we can say |f(x)|≤c|g(x)|.........(1)…

Q: Prove valid. (x) ( ~ Ax > Dx)                                                  / (Ex) (Ax v Bx) (Ey)…

A: Below is the answer to above question. I hope this will helpful for you..

Q: INPUT: A graph G, a non-negative integer k ≥ 0, and a boolean formula F in CNF.  OUTPUT: “Yes” if…

A: To prove that this problem is NP-Complete, we will use a reduction from the 3-SAT problem. Given a…

Q: Parameter Estimation + Confidence Interval + Margin of Error Means when o is known Problem#2 23. A…

A: Set the population standard deviation (sigma) and the sample mean (r). For part (a), compute the 96%…

Q: Draw the state space tree for the 5-Queen problem with a branching factor of 2. Show a local maxima…

A: This demonstrates the concept of a local maxima in the state space tree of the 5-Queen problem and…

Q: Prove or disprove that for any x ∈ N, x(x+1)/2 ∈ N (where N = {0, 1, 2, 3, ….}

A: Hello student

Q: Write algorithm monien–speckenmeyer(F, x)?

A: algorithm for monien–speckenmeyer(F, x):-

Q: Subject: Design Analysis and Algorithm Please write handwritten Answer AndExplain Briefly Please…

A: The key idea behind the proof is to show that the undirected Hamiltonian cycle problem can be…

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If…

A: Solution for following question - Given, n=3 The roots of the function are 3 and 2i are zeros.

Q: Pis the set of problems that can be solved in polynomial time. More formally, P is the set of…

A: A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in…

Q: Consider nonnegative integer solutions of the equation x1+x2+x3+x4+x5+x6=30. How many different…

A: Answer 1 There are 462 different solutions. Answer 2 C(15,6)=5005 different solutions exist.

Q: Solve this Problem using Jupyter Notebook 2. Use of SciPy must be demonstrated in your solution 3.…

A: Algorithm : - Importing the necessary libraries, tha will the scipy library to solve the…

Q: You are given a graph G, and the problem is to test whether there is a cycle of length at most 1000…

A: To solve this problem, DFS (Initial Search Depth) can be used effectively. By using DFS we obtain…

Q: Prove by natural deduction: Show ∃x[p(x) ∧ q(x)] ⊧ ∃xp(x) ∧ ∃xq(x)

A: Prove by natural deduction: Show ∃x[p(x) ∧ q(x)] ⊧ ∃xp(x) ∧ ∃xq(x)
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Q: Knight-Knave problems A very special island is inhabited only by knights and knaves. Knights always…

A: In the realm of logical puzzles, Knight-Knave problems present captivating challenges that require…

Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.