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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Students have asked these similar questions
Convert the following set of sentences to clausal form:
S1: A (B V E)
S2: E =D
S3: CAF= -B
S4: E = B
S5: B = F
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)
Convert the following predicate calculus to English sentence.
(∀X) (dog(X) → barks(X))
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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- Let C(x) be the statement “x has a cat,” and let D(x) be the statement “x has a dog.” Let the domain consist of all students in this class. Express each of the following propositions in regular sentences.(a)∀x(C(x)→D(x)) (b)∀x(¬C(x)→D(x)) (c) (∃xC(x))∧(∀xD(x)) (d)∀x(C(x)⊕D(x))arrow_forwardIn the context of Propositional Logic, using letters to denote sentences components, translate the following compound sentences into symbolic notation. In the translation indicate clearly the meaning of each propositional letter: A. Roses are red and violets are blue. B. Whenever violets are blue, roses are red and sugar is sweet. C. Roses are red only if the violets are not blue and the sugar is sour. D. Roses are red and if sugar is sour then violets are not blue or sugar is sweetarrow_forwardUsing the predicate symbols shown and the appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a bee. F(x): x is a flower. L(x, y): x loves y All bees love all flowers which one from this Group of answers is the correct a. (∀x)(B(x) → [(∃y)(F(y) ∧ L(x, y)] b. (∀x)(B(x) → [(∀y)(F(y) ∧ L(x, y)] c. (∀x)(B(x) → [(∀y)(F(y) → L(x, y)] d. (∀x)(B(x) ∧ [(∃y)(F(y) → L(x, y)]arrow_forward
- 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.arrow_forwardLet p, q and r be propositions: p: Jasper has sore eyes q: Jasper misses the last day of the board exam r: Jasper passes the board exam Write the following propositions in terms of the given connectives: a.) q→¬r b.) q ↔ p c.) p → q ⋀ ¬rarrow_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 semantic tableaux to show if these are invalid: ¬(p⊃q)∧¬(p⊃r)⊢¬q∨¬r p∧(¬r∨s),¬(q⊃s)⊢r ¬(p∧¬q)∨r,p⊃(r≡s)⊢p≡q p⊃(q∧r),¬r⊢¬parrow_forwardFor this question about predicate logic, please note that, even though the 'nonsense' words are only nouns and verbs, you do not need to know the meaning of the words being used in order to answer this question. Consider a universe of discourse that contains (among other things) all gudgeons. If the predicates B(x), C(x), and G(x) represented the assertions x brabbles, x corrades, and x groaks, respectively, then which of the following would be an accurate translation of the following assertion? some gudgeons do not brabble even though they corrade and groak Select one: (-B(=) ^ C(z) ^ G(x)) O none of these options (-B(2) v C(x) V G(=)) O Vz (-B(x) ^ C(2) V G(z) O I (¬B(x) V C(x) ^ G(x)) (-B(2) ^ C(x) V G(=)) (-B(=) ^ C(x) V G(=) O Frarrow_forwardFor this question about predicate logic, please note that, even though the 'nonsense' words are only nouns and verbs, you do not need to know the meaning of the words being used in order to answer this question. Consider a universe of discourse that contains (among other things) all gudgeons. If the predicates K(x), G(x), and J(x) represented the assertions x kenchs, x groaks, and x jargogles, respectively, then which of the following would be an accurate translation of the following assertion? if any gudgeon kenchs or that gudgeon does not groak then that gudgeon does not jargogle Select one: ((K(=) v G(2) → J(=) IE O (K(e)v -G(=) O Væ V → ¬J(x) (K(=) ^ -G(2)) → ¬J(x) TE O → ¬J(x) O none of these options (Ke)v -G(=) O Va V V ¬J(x) (K(2) V -G(2) v V ¬J(x)arrow_forward
- Below are some predicates and their corresponding statements: p(x): x is a student in your class q(x): x has taken a course in logic programming Here, the domain for quantifiers consists of all people. Choose the correct proposition for the sentence: All student in your class has not taken a course in logic programming. a. ∀x¬(P(x) → Q(x)) b. ∀x(P(x) → ¬Q(x) c. ¬∀x (P(x) → Q(x)) d. ¬∃x(P(x) ∧ Q(x))arrow_forward1. Explain the difference between first-order logic and propositional logic. 2. The language of first-order logic is based on objects and relations. An example of a first-order logic expression is "squares near the WAMPUS are smelly." What are the objects and relations in that expression? 3. What is an atomic sentence? Give an example. 4. What is the universal quantifier? Write the sentence "All kings are persons" using the universal quantifier and other logic symbols. Hint: To find the logic symbols in blackboard click on fx from the toolbar above and select the symbols tab. 5. What is the existential quantifier? Write the sentence "There is a prime number that is even" using the existential quantifier and other logic symbols.arrow_forwardComplete the truth table for the following compound statement.(p∨∼q)→(r∧∼p)(p∨∼q)→(r∧∼p) p q r ∼q∼q p∨∼qp∨∼q ∼p∼p r∧∼pr∧∼p (p∨∼q)→(r∧∼p)(p∨∼q)→(r∧∼p) T T T T T F T F T T F F F T T F T F F F T F F F Is the compound statement a tautology? No, the statement is not a tautology. Yes, the statement is a tautology.arrow_forward
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