Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 7, Problem 6E
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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);
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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).
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Draw the truth table of (A→ B) ˄ (B → A) and (A Ú B) ˄ (¬B Ú A). Determine from the truth table whether (A→ B) ˄ (B → A) is logically equivalent to ((¬A Ú B) ˄ (¬B Ú A)
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 f(x)=ax+b and g(x)=cx+d, where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that f◦g=g◦f.arrow_forwardTo do this, either show that both sides are true, or that both sides are false, for exactly the same combinations of truth values of the propositional variables in these expressions (whichever is easier). Show that (p→r)∨(q→r) and (p∧q)→r are logically equivalentarrow_forward3. Prove ⊢ (¬A → A) → A in Hilbert deductive system. Note: In addition to the axioms and rule of inference of H, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook). You may not use theorem 3.31, as this is precisely that theorem.Theorem 3.20 ⊢ ¬A → (A → B). Theorem 3.21 ⊢ A → (¬A → B). Theorem 3.22 ⊢ ¬¬A → A. Theorem3.23 ⊢A→¬¬A.Theorem3.25 ⊢(A→B)→(¬B→¬A).Theorem3.28 ⊢(¬A→false)→A.Rule 3.29 (Reductio ad absurdum) Theorem3.30 ⊢(A→¬A)→¬A. Prove {¬A} ⊢ (¬B → A) → B in H. Note: In addition to the axioms and rule of inference of Hilbert deductive system, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook).arrow_forward
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- A 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 α be any logical truth and let β be any proposition. Explain why ¬α ∨ β isequivalent to β.arrow_forwardGiven A = {1,2,3} and B={u,v}, determine. a. A X B b. B X Barrow_forward
- b) Given the following relations: A B C 1 5 7 4 9 r a TU В 8 10 6 11 S A В μ D 4 12 Find (i) the Cartesian product of r and s (rx s). (ii) the Cartesian product of r and s and then performing a selection operation on the result with the predicate r.A = s.A (Or.A-s.A (r x S)). (iii) the projection of A,C from relation r (IIA.c (r)). E 6 8arrow_forwardLet 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_forwardUse a truth table to demonstrate that these two statements are logically equivalent:((p ∧ ¬q) ∨ (p ∧ q)) ∧ q and (p ∧ q).arrow_forward
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