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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Check out a sample textbook solution
Students have asked these similar questions
Q1 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.…
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
- 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 Farrow_forwardDetermine whether statement forms p ∧ (q ∨ r) and (p ∧ q) ∨ (p ∧ r) are logically equivalent.Justify your answer.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
- Please help me with this question, also respect the exemple please. Thank youarrow_forward1. 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_forwardClassify the following sentence as True or False: Reichenbach’s causation definition solves the problem of Alternative Explanations.arrow_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_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_forwardUse 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_forward
- Determine 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_forwardProof: ⊤ ⊢ (A ∧ ¬B) → ¬(A → B) Please indicate assumption, intro, or elimination, with the line number operated.arrow_forwardConsider the following set of premises and conclusions. Assume all variables are statement variables. a. p V q b. q →r C. pAs →t d. ~r e. ~g → u A S f. :it Deduce the conclusion from the premises by applying the valid argument forms listed in Table 2.3.1 in Section 2.3. Use the same format for the steps of the deduction as in Example 2.3.8. Step 1 of the deduction could be the following. by premise (b) by premise (d) by modus tollens Fill in the blanks for Step 2 of the deduction. p vq by ---Select--- v by ---Select--- v :p by Select--- Complete the steps of the deduction, including reasons, and submit your work as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosenarrow_forward
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