Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 7, Problem 5E
a.
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Valid statement
- Alpha is valid if and only if True|= alpha...
b.
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Valid statement
- For any alpha, False|= alpha...
c.
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Valid statement
- It is true if and only if the sentence is valid...
d.
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Valid statement
- It is true only if the sentence is valid...
e.
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True statement
- It is true because the right hand side is
f.
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Valid statement
- It is true if and only if the sentence is unsatisfiable...
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Consider the two expressions σθ(E1 ⟕E2) and σθ(E1 ⋈ E2).Give a simple condition on the predicate θ, which if satisfied will ensure that the two expressions are equivalent.
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Q" is true. This shows that the domain of the quantifier matters. Now, give your own sim-
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Consider the following narration:
If gender equality is to be achieved then patriarchy must be dismantled. If patriarchy is dismantled then matriarchy should be discouraged. If matriarchy is discouraged then gender equality is not to be achieved. Patriarchy is not going to be dismantled. Therefore, gender equality is not to be achieved
a) Encode the argument in Propositional Calculus.
b) As a result of a) above, use logical rules of inference to show that the given argument is sound/valid. HINT: For any statement forms, P and Q
P ---> Q = ¬Q ---> ¬P
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- Consider the following narration: If gender equality is to be achieved then patriarchy must be dismantled. If patriarchy is dismantled then matriarchy should be discouraged. If matriarchy is discouraged then gender equality is not to be achieved. Patriarchy is not going to be dismantled. Therefore, gender equality is not to be achieved a) Encode the argument in Propositional Calculus. b) As a result of a) above, use logical rules of inference to show that the given argument is sound/valid. HINT: For any statement forms, P and Q P - Q=-Q- -P.arrow_forwardConsider the following arguments, in each case determine whether the argument is valid, i.e., is it an instanceof an argument form in deductive logic in which the rule of inference is truth-preserving?(a) 1. p2. (p ∨ s) (b) 1. ¬(r ∨ s)2. ((r ∨ s) ∨ p)3. p (c) 1. (¬r ∨ ¬s)2. ((p ∨ q) → (r ∧ s))3. ¬(p ∨ q) (d) 1. (p → ¬¬p)2. (¬¬¬p ∧ ¬p)3. ¬p4. (¬p ∨ q)arrow_forwardProve each statement by contrapositivearrow_forward
- 1. In transforming a formula into an equivalent CNF, you can use the absorption laws to eliminate conjunctions within disjuntions, i.e. expressions such as p ˅ (q ˄ r) and (p ˄ q) ˅ r. True False 2. Let p, q, and r be propositional variables. Which of the following expressions would NOT be formulas in conjunctive normal form? (p ˄ ¬q) ˅ (¬r ˄ q ˄ p) ¬q p ˅ q ˅ ¬p p ˄ ¬p 3. Consider the propositional logic formula (p ˄ q) ˅ (r ˅ ¬s) From the options below, which one is the equivalent CNF? To determine the correct answer, transform the formula above into CNF using the steps learnt in this module. (p ˅ r ˅ s) ˄ (q ˅ r ˅ ¬s) (¬p ∨ r ∨ s) ∧ (¬q ∨ ¬r ∨ ¬s) (p ˅ r ˅ ¬s) ˄ (q ˅ r ˅ s) (p ˅ r ˅ ¬s) ˄ (q ˅ r ˅ ¬s)…arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Computer science. The j-th companion can be set before the I-th companion on the photograph if his square shape is lower and smaller than the square shape of the I-th companion. Officially, somewhere around one of the accompanying conditions should be satisfied: hj<hi and wj<wi (the two companions are standing or both are lying); wj<hi and hj<wi (one of the companions is standing and the other is lying). For instance, on the off chance that n=3, h=[3,5,3] and w=[4,4,3]: the main companion can be set before the second: w1<h2 and h1<w2 (one of the them is standing and the other one is lying); the third companion can be put before the second: h3<h2 and w3<w2 (the two companions are standing or both are lying). In different cases, the individual in the closer view will cover the individual behind the scenes. Help Polycarp for every I find any j, with the end goal that the j-th…arrow_forwardProposition (Distributive Law): For expressions P1, P2, P3, any word matching the regular expression (P1(P2|P3)) also matches the regular expression ((P1P2)|(P1P3)) Give a proof of the above proposition, or demonstrate that it is false.arrow_forward
- For (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was green skin, then "b" being the Hulk would make this true. Am example of this being false would be: If the domain was all integers and x was positive, even integers and "b" was integers greater than zero.arrow_forwardA detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that: If the handyman is lying, then so is the butler. The gardener and the handyman cannot both be telling the truth. The cook and the gardener are not both lying. The handyman is telling the truth only if the cook is lying.arrow_forwardLet P(x,y) be the statement “x and y work at the same company” and Q(x,y) be the statement “x and y uses the same programming language”. Which of the following sentences expressses ∀x∃y((x≠y)∧P(x,y)∧Q(x,y))? 1. For all companies, there exist two employees who uses the same language. 2. For all employees using the same languages, there exist another employee who work at his company. 3. For all employees of all companies, there exist another employee who uses the same language. 4. For all employees, there exist another employee in the same company who uses the same language.arrow_forward
- Let P be “this book is a non-fiction book” and Q be “the ideas in the book is consistent with physical reality.” Consider a case where both P and Q are false (e.g. a fantasy novel and an unrealistic phenomenon in the novel) and see whether it makes sense that P→Q is true. [Give an example, i.e., the name of a book and a particular idea in that book] Explain why it is possible that P→Q is true yet Q is false. [Type your explanation]arrow_forwardQl: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.arrow_forwardDirections: Let A = {1, 2, . . . , 9, 10}. Consider each of the following sentences. If it is a statement, then determine its truth value. If it is a propositional function, determine its truth set.arrow_forward
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