Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Expert Solution & Answer
Chapter 7, Problem 18E
a.
Explanation of Solution
Truth table
- A simple truth table has eight rows...
b.
Explanation of Solution
Results
- For the left-hand side:
(Food ⇒ Party) ∨ (Drinks ⇒ Party)
(￢Food ∨ Party) ∨ (￢Drinks ∨ Party)
(￢Food ∨ Party ∨ ￢Drinks ∨ Party)
(￢Food ∨ ￢Drinks ∨ Party)
- For the right-ha...
c.
Explanation of Solution
Resolution
- For proving a sentence is valid, then the negation is unsatisfiable...
Expert Solution & Answer
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Students have asked these similar questions
Complete the truth table for the implication. You must submit a complete TT. (A ∧ ~B) → C.
A
B
C
(A ∧ ~B) → C
T
T
T
T
T
F
T
F
T
T
F
F
F
T
T
F
T
F
F
F
T
F
F
F
Question 3
VX(P(X) v Q(X))→ (VXP(X) V VXQ(X))
The above expression follows from the valid argument forms of logic and
the rules for quantifiers.
True
False
Question 4
Give an interpretation (in words) of the predicates in the previous question
that shows you understand why your answer is correct.
Are you sure that the negation of the premise is ∃x(Px ∧ ¬∀yPy)? Would it not just be ¬∀x(Px ∧ ¬∀yPy)?
Chapter 7 Solutions
Artificial Intelligence: A Modern Approach
Ch. 7 - Suppose the agent has progressed to the point...Ch. 7 - (Adapted from Barwise and Etchemendy (1993).)...Ch. 7 - Prob. 3ECh. 7 - Which of the following are correct? a. False |=...Ch. 7 - Prob. 5ECh. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - We have defined four binary logical connectives....Ch. 7 - Prob. 9ECh. 7 - Prob. 10E
Ch. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - Prob. 14ECh. 7 - Prob. 15ECh. 7 - Prob. 16ECh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - A sentence is in disjunctive normal form (DNF) if...Ch. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27E
Knowledge Booster
Similar questions
- Determine whether statement forms p ∧ (q ∨ r) and (p ∧ q) ∨ (p ∧ r) are logically equivalent.Justify your answer.arrow_forwardQ1 Show that the argument form with premises (p A t) →(r V s), q → (u ^ t), u →p, and ¬s and conclusion q→r is valid by using rules of inference from Table 1. Q2 For each of these arguments, explain which rules of inference are used for each step. a) "Linda, a student in this class, owns a red convertible. Everyone who owns a red convertible has gotten at least one speeding ticket. Therefore, someone in this class has gotten a speeding ticket." b) "Each of five roommates, Melissa, Aaron, Ralph,Veneesha, and Keeshawn, has taken a course in discrete mathematics. Every student who has taken a course in discrete mathematics can take a course in algorithms. Therefore, all five roommates can take a course in algorithms next year." c) "All movies produced by John Sayles are wonderful. John Sayles produced a movie about coal miners. Therefore, there is a wonderful movie about coal miners." d) "There is someone in this class who has been to France. Everyone who goes to France visits the Louvre.…arrow_forwardPlease help me with this question, also respect the exemple please. Thank youarrow_forward
- Truth Table For the following proposition, indicate whether it is a tautology, a contra-diction or neither. Show the solution in a truth table/ (-B-A)-> ((-B -> A) ->B)arrow_forwardClassify the following sentence as True or False: Reichenbach’s causation definition solves the problem of Alternative Explanations.arrow_forwardUsing the same defifinitions as in the previous question, translate each of the following predicate logic statements into English. Try to make your English translations as natural sounding as possible. These statements appear long, but try to break them into smaller cohesive pieces. ∀w ∈ K,(T(w) ∧ W(w)) →(∃p ∈ K, P(p) ∧ S(p) ∧ I(p) ∧ A(p, w)). 2. ∃k ∈ K, ∃r ∈ K, k =r ∧ T(k) ∧ T(r) ∧ F(k, r) ∧ F(r, k) ∧ (∀z ∈ K, Z(z) → A(z, k)). 3. ∃t ∈ K, T(t) ∧ W(t) ∧ ∃x ∈ K, ∃y ∈ K, x = y ∧ Z(x) ∧ W(x) ∧ Z(y) ∧ W(y) ∧ A(t, x) ∧ A(t, y) ∧ (∀w ∈ K,(x = w ∧ y = w ∧ Z(w) ∧ W(w)) → ∼ A(t, w))arrow_forward
- 1. Construct a detailed truth table for the following propositional statement: (((P ∨Q)∧¬P)→Q) Is it a tautology? 2. Construct a detailed truth table for the following propositional statement: (P ∧ Q) → R Is it a tautology?arrow_forwardDetermine whether these statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. p ꓥ t and parrow_forwardConstruct a truth table to determine the truth value of the compound proposition (A ∧ B) ∨ (¬C ∧ D) where A, B, C, and D are propositional variables.arrow_forward
- Use De Morgan’s Laws, and any other logical equivalence facts you know to simplify the followingstatements. Show all your steps. Your final statements should have negations only appear directly nextto the sentence variables (P, Q, etc.), and no double negations. It would be a good idea to use onlyconjunctions, disjunctions, and negations.(a) ¬((¬P ∧ Q) ∨ ¬(R ∨ ¬Q)).(b) ¬((¬P → ¬Q) ∧ (¬Q → R)) (careful with the implications).(c) For both parts above, verify your answers are correct using truth tables. That is, use a truth tableto check that the given statement and your proposed simplification are actually logically equivalent.arrow_forwardProof: ⊤ ⊢ (A ∧ ¬B) → ¬(A → B) Please indicate assumption, intro, or elimination, with the line number operated.arrow_forwarduse propositional logic to see if the argument is valid (A ∧ B) ∧ (B → A’) → (C ∧ B’) A ∧ B Hypotheses B → A’ Hypotheses Chart to go off of attached belowarrow_forward
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