Q. Consider the following instance of 3-SAT problem: (x1 v X2 V -X3) ^ (xı V ¬X2 V ¬X3) ^ (¬X1 V –¬X2 V X3) ^ (¬xi V ¬X2 V ¬X3) and reduction from 3-SAT to CLIQUE. What is the instance of CLIQUE problem that corresponds to the above instance of 3-SAT? If the above instance of 3-SAT is YES instance, show a certificate, verifying this, and also corresponding certificate of the CLIQUE problem.

Q: aven the folIlowing matrix: X= 16 3 2 13 5 4 8 7 Write the result of the following: 1- >> x(:,2) 2-…

A: Please note we can only answer 3 subparts per question. Please post the rest in a different…

Q: D = {(¬A v C) V ¬B} ^ {[(A ^ B) ^ (¬B ^ C)] v [¬AV C] V [¬B^ C] v [(A ^ B) ^ (¬A v C)]}

A: Truth table for given statement: A     B     C      ¬A    ¬B      ¬AvC     (¬AvC )v¬B       A^B…

Q: 4. Let r = (¬Vv, Pv, Pvz, Pvz...). Is r consistent? Is F satisfi- able?

A: Answer: I have given answer in the handwritten format.

Q: Consider the following set of FD's: F = {A → B, B → A, A → C, C → A}. Which of the following sets of…

A: To be a canonical cover of an FD it must follow 3 rules: 1) Singleton RHS {means  X->YZ  this…

Q: Please answer the following question in depth with full detail. Suppose that we are given an…

A: Heuristics are a frequent strategy used in artificial intelligence to solve complex issues. An…

Q: Which of the following is logically equivalent to (p ∧ q ∧ r) ∨ (p ∧ q ∧ ￢r) ∨ (p ∧ ￢q ∧ r) ∨ (p ∧…

A: Equation is (p ∧ q ∧ r) ∨ (p ∧ q ∧ ￢r) ∨ (p ∧ ￢q ∧ r) ∨ (p ∧ ￢q ∧ ￢r) ∨ (￢p ∧ ￢q ∧ r). We brake the…

Q: Problem 03: (a) Use a truth table to determine whether the statements (pv-q) ^ (pv q) and ~p V (p ^…

A: The following question certains to boolean logic, a fundamental concept in computer science and…

Q: Q-1: a) let p, q andr be propositions. Simplify the following compound proposition: (¬r) ^p^q) V…

A:

Q: 49. Establish these logical equivalences, where x does not oc- cur as a free variable in A. Assume…

A: solution

Q: Would you be able to help me address this problem and its related elements? Please offer a detailed,…

A: The objective of the question is to prove that the language ALL_DFA, which consists of all…

Q: What type is inferred for a, ß, and for the variable xs? let xyz (a : a) : B %3D let rec abc a match…

A: Answer: I have given answered in the  brief explanation

Q: onsider the challenge of determining whether a witness questioned by a law enforcement agency is…

A: BELOW STEP BY STEP COMPLETE SOLUTION REGARDING YOUR PROBLEM WITH EXPLANATIONS :

Q: Consider f : X Y, with domain X = {l,a, z,0, 8, m, c, e, g, d, u, v} and codomain Y = {44,35,67, 45,…

A: Hey there, I am writing the required solution based on the above given question. Please do find the…

Q: Suppose you want to solve the following equality 2a + b + 3c + 4d + 6e = 45 What is the chromosome…

A: Suppose there is equality 2a + b + 3c + 4d+6e = 45, genetic algorithm will be used to find the value…

Q: There are n issues numbered with integers from 1 to n. I-th issue has the intricacy ci=2i, label…

A: Here have to determine about the numbered with integers programming problem statement.

Q: L2 = {1ª01ª0ª 10ª | a ≥ 0} 5. () Using L₂ from the previous problem, is L₂ € Eo? Circle the…

A:

Q: Exercise. In this exercise, you will examine the changes to the analytic step response of a transfer…

A:

Q: 5. Consider the same instance of 3-SAT problem: (x1 V X2 V ¬X3) ^ (x1 v ¬X2 V ¬X3) ^ (¬Xı v ¬X2 V 3)…

A: Given an instance of 3-CNF-SAT where P=C1^C2^C3^...….^Ck is a Boolean formula with k clauses. With…

Q: Would you be able to help me address this problem and its related elements? Please offer a detailed,…

A: The objective of the question is to prove that the language ALL_DFA, which consists of all…

Q: Problem 8 (#2.2.8).Prove the idempotent laws by showing a) A∪A=A. b) A∩A=A.

A:

Q: Let C (x, y) =" x likes y "and domain of x and y are all people. Then the statement "There are…

A:

Q: Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G 3.Use all three of…

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: Which  is the logically equivalent to (p ∧ q ∧ r) ∨ (p ∧ ￢q ∧ r) ∨ (￢p ∧ q ∧ r) ∨ (￢p ∧ q ∧ ￢r) ∨…

A: Here the given expression is: (p ∧ q ∧ r) ∨ (p ∧ ￢q ∧ r) ∨ (￢p ∧ q ∧ r) ∨ (￢p ∧ q ∧ ￢r) ∨ (￢p ∧ ￢q ∧…

Q: i need help soving this?  let U = {a, b, c, d, e, f, g, h, k}, A = {a, b, c, g}, B = {d, e, f, g},…

A: Answer the above question are as follows

Q: Complete the truth table and determine whether or not the following statement is a tautology, a…

A: Tautology & Contradiction : Tautology and contradiction are two types of logical statements. A…

Q: Is the following argument valid or not? I recommend an abbreviated table. -P(a) ^ (¬Q(b) v Q(c)),…

A: Correct Answer is Option ("D") i.e... It is invalid Explanation: It is a validity of a statement it…

Q: Question 5: arange Implement the function arange, which behaves just like np.arange(start, end,…

A: Program Approach: Step 1: Create a function arange(start,end,step) with 3 parameters start, end and…

Q: when p and q are both true propositions while r is fale. which of the following has truth value of…

A: Here in this question we have given four Expression and given p=TRUE q = TRUE  r=FALSE. we have to…

Q: B. Construct the mathematical statement of the following. (8-14) •P = "JR comes to the party" •Q =…

A: Solution: CK comes only if KL comes means S->R. This implies either 1st option is correct or the…

Q: 1.) If f(x) = 2.x^2 - x + 5. What is f(-3)? 2.) If A = {a, b, d, e}, B = {b, c, e, f} and C = {d,…

A:

Q: Consider the deterministic finite automaton M = (Q, E, 8, 8, F) where Q = {0, 1, 2, 3, 4, 5}, Σ =…

A: A representation of a finite automation with the fewest number of states that maintains the same…

Q: 3. Show that the identity sin²(x) = 1-cos(2x) 2 holds for the following values of x. π a) x = 3 b) x…

A: NOTE : Since programming language is not mentioned. Therefore answering in MATLAB.   The code shows…

Q: The sets A and B are defined as follows: A = {x € R5 : max (| − x1 + 2x2 + x3 − X4|, x1 + x² − x5) ≤…

A: The basic and feasible solution would be provided by the users to solve the Linear programming…

Q: A valid argument is given below. Fill in the missing values of the proof. vx (P(x) → (Q(x) v R(x)))…

A: Here, a proof applying the predicate logic is given. The task is to fill the missing values to the…

Q: Consider the following formula in the usual language of Set Theory L= {e} (recall that e is a binary…

A: Here variable x and z are associated with some quantifier.  This means variable x and z are bounded.…

Q: w| w = t1 #t2 # · · · #tk for k ≥ 0, each t i ∈

A: Let Y = {w| w = t1 #t2 # · · · #tk for k ≥ 0, each t i ∈ 1* , and ti != tj whenever i != j}. Here…

Q: I'm having a difficult time with this problem. Could you lend me a hand in understanding it? I'd…

A: Approach to solving the question: Let's break down the problem step by step.1. Definition of…

Q: QUESTION 4 Which of the following is a negation of the statement ((X)O^(X) dL)XA ((X)0L V (X)d)XA…

A: The first question asks to find the negative of the first-order logic & the second question asks…

Q: 2. A = {[(P → Q) ^R] v ¬Q} → (QAR)

A: The answer is:

Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…

A: EXPLANATION: Composition of function is basically the application of one kind of function to the…