To transform any formula into a Conjunctive Prove that the procedure normal form preserves satisf...
6. Obtain disjunctive normal form, conjunctive normal form, for the following expression 7. Prove that there are no solutions in integers x and y to the equation x +4y 12
Transform the following formulas into conjunctive normal
form:
a. A ∧ (A ⇒B)
⇒ B
b. A ∧ B ⇔ A
∨ B
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form (CNF) formula where the pure literal rule can be applied, but the unit propagation rule cannot. The formula must have at least 3 clauses. [3 marks
(b) Using the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, determine whether the following formula is satisfiable. Show each step. [3 marks] (c) Give an example of a conjunctive normal form...
6. Obtain disjunctive normal form, conjunctive normal form, for the following expression
Convert the propositional statements into Conjunctive Normal Form in JAVA. Use the algorithm given in this PDF: http://swtv.kaist.ac.kr/courses/cs402-07/prop_logic4.pdf The implementation must have the following classes Solver.java: Contains the main solving method to solve a formula in conjunctive normal form. A formula is a LinkedList. Clause.java : A clause represents disjunctions of literals. A clause is represented as a Hashmap which allows fast access to a literal with a given name. Literal.java: A literal represents an atom that is either negated...
Convert the following to conjunctive normal form. Show your work and state what steps are used (i.e. De Morgan's, implication removal, etc). 1. ((S+Q)+((-SAQ)VW)) 2. ((-QVS)V(-Q+(SAW)))
DNF-SAT is the satisfiability problem for Boolean formulae in disjunctive normal form (DNF). A formula in DNF is a disjunction of anticlauses A1 ∨ A2 ∨ · · · ∨ Ak , where each Ai for 1 ≤ i ≤ k is a conjunction l1 ∧ l2 ∧···∧ lji of literals. 1. What is wrong with the following argument? CNF-SAT is polynomial-time reducible to DNF-SAT, since ∧ and ∨ each distribute over the other. For example, (x1∨x2)∧(x1∨x3) can be rewritten...
3. There are an infinite number of possible normal distributions and we use the formula z = (x - m)/ s where m = mean and s = standard deviation, to convert values from any normal distribution to the standard normal distribution. We then calculate the answer in terms of the standard normal distribution and say that the answer we got is also the answer for the normal distribution we were working with. Why are we allowed to do that?...
First Order Logic We would like to find out more information about a very shady organization called the Society of Americans for Nepotism. We already know the following facts about this organization: sally and ellen are members. ellen is related to bill. Anyone related to a member is also a member. Being related is symmetric (i.e., if X is related to Y, then Y is related to X) bob is not a member. a. Represent these facts as sentences in...
THE EMPIRICAL FORMULA OF SELECTED HYDRATES experiment PROCEDURE THIS EXPERIMENT SHOULD BE DONE IN PAIRS. 1. Available to you should be: a Büchner funnel, a rubber funnel adapter, side-arm filter flask, thick-walled rubber tubing, plastic forceps and a plastic spatula. 2. Before you turn the hotplate on, wipe the hotplate down with a damp paper towel. During this experiment you will be placing filter paper containing products directly onto the surface of the hotplate. As such, you will want to...