Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 7, Problem 7E
a.
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- Sentence is false only if B and C are false...
b.
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- Sentence is false only if A, B, ...
c.
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- The last four conjuncts specify a mo...
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Let p, q, and r be the propositions p: You started a new video game this week. q: You finished all its quests.r: You didn’t win the platinum trophy.Express each of these propositions as an English sentence.¬p → ¬q(p ∧ q) → (¬r)((¬p) → (¬q)) ∨ (q → (¬r))(p ∧ q) ∨ (¬q ∧ r)
Module 6 Journal. Please complete each of the proofs below. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. (D→C) • (C→ D), E → -(D → C) :. -E F • (G V H), -F V -H : F. G -U → ~B, S → ~B, ~(U • -S), TV B .:. T 3. (QR) V (-Q • -R), N → ~(Q ↔ R), EV N.. E -X → -Y, -Xv -Y, Z →Y: -Z -M V N, -R→-N : M → R
Tick each statement that is valid.
Select one or more:
a. ¬(C → (D → C)) is unsatisfiable.
b.
AV-Bv CV DVE V F V¬A is a tautology
(¬B → B) → (B → C) is a tautology
AV (B → C) v (D → E) v ¬A is a taulogy.
e. (U → U) → U is a tautology.
P→ Q and¬P ^ Q are logically equivalent
g. TVW V-T is a tautology
C.
f.
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
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- 1. Let p be “It is cold” and let q be “It is raining”. Give a simple verbal sentence which describes the statement: a) q ∨ ~p 2. Construct the truth table of (p ∧ q) ∨ (q ∧~r).arrow_forwardConvert the following set of sentences to clausal form: S1: A (B V E) S2: E =D S3: CAF= -B S4: E = B S5: B = Farrow_forwardConvert the following predicate calculus to English sentence. (∀X) (dog(X) → barks(X))arrow_forward
- if p and q are logical variables, which of the following is a tautology (i.e., always correct irrespective of specific value of variables) Select one: a. p → (q ∧ p) b. p ∨ (q → q) c. (p ∨ q) → q d. p ∨ (p → q)arrow_forwardSee the image. a.Construct a context-free grammar generating C.Explain how your construction accounts for each rule. b.We could eliminate one rule from Cand make it regular. Which rule would that be, and why would it work? You do not need a formal proof, but you do need an explanation.arrow_forwardSelect ALL the sentences of FOL. G(P) AxLikes(x,pia) G(p) Pia AxLikes(x,y) AxGuilty(x) Guilty(x)arrow_forward
- 2. For each of the following statements, push all negations (¬) as far as possible so that no negation is to the left of a quantifier (in other words, the negation is immediately to the left of a predicate). Show your work. (az(A(x, z) ^ B(y, z)) (b) y(xA(x, y) → EzB(z, y)) (c)¬\x((³yA(x, y) → ]yB(x, y)) → ¬³yС(x, y))arrow_forward3. Write a sentence that is true in an interpretation A if, and only if, the domain of A contains exactly two elements. 4. Write a sentence that is true in an interpretation A if, and only if, the domain of 2A contains exactly three elements.arrow_forwardIn the simplified English grammar of the given Figure, there are only finitely many legal sentences. How many are there? Why? (1) sentence → noun-phrase verb-phrase . (2) noun-phrase → article noun (3) article →→ a | the (4) noun → girl | dog (5) verb-phrase verb noun-phrase (6) verb → sees | petsarrow_forward
- Formalize the following sentence in english: aX. elephant(X)| onarrow_forwardFormalize the following sentence in english: Vx. (person(x ) A ay. (like(x,y) ^ food(y) A¬contain(cheese)))arrow_forwardComplete the following exercises about logical sentences:1. Translate into *good, natural* English (no xs or ys!): ∀x,y,lSpeaksLanguage(x,l)∧SpeaksLanguage(y,l)⟹Understands(x,y)∧Understands(y,x). Explain why this sentence is entailed by the sentence ∀x,y,lSpeaksLanguage(x,l)∧SpeaksLanguage(y,l)⟹Understands(x,y). Translate into first-order logic the following sentences:1. Understanding leads to friendship.2. Friendship is transitive.Remember to define all predicates, functions, and constants you usearrow_forward
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