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 14E
a.
Explanation of Solution
Correct representation
- The given first sentence asserts since all conservatives are radical.
- This is not what was stated.
- The next sentence is a correct representation of assertion...
b.
Explanation of Solution
Sentence in horn form
- The first sentence is in horn form.
(R ∧ E) ⇐⇒ C ≡ ((R ∧ E) ⇒ C) ∧ (C ⇒ (R ∧ E)) ≡ ((R ∧ E) ⇒ C) ∧ (C ⇒ R) ∧ (C ⇒ E)
- The second sentence is also in horn form...
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Students have asked these similar questions
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)
Proposition (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.
Let 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 ⋀ ¬r
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
- 1. Which of the following statements are true? (a) |N|=|Z| (b) |N|<|Z| (c) |Z|=א0 (d) |R|>|Z| 2. Which of the following statements are tautologies? (a) P → Q (b) P ∧ ¬P (c) P ∨ ¬P (d) P → P 3. The contrapositive equivalency of ¬Q → P is given by: (a) P → Q (b) Q → P (c) ¬P → Q (d) ¬Q→Parrow_forwardThis question was on a homework assignment which I could not complete before the deadline. Show that whether the following propositions is a tautology, satisfiable but not a tautology, or a contradiction. If it is a tautology or a contradiction, please give the proof. If it is satisfiable, please give a true assignment and a false assignment. (A ∨ B ∨ ¬C) ∧ (A ∨ ¬B ∨ D) ∧ (A ∨ ¬C ∨ ¬D) ∧ (¬A ∨ ¬B ∨ ¬D) ∧ (A ∨ B ∨ ¬D)arrow_forwardSimplify the following assertions (so that ¬ does not appear). a) ¬((∃a ∈ A,((∀b ∈ B, a × b = 2) ⇒ (∃b ∈ B, a + b ≠ 3))) & (∀a ∈ A, ∃b ∈ B, ((a+b = 5)∨(a−b = 5)))) b) ¬((∃a ∈ A, ∀b ∈ B, ((a + b = 3) ∨ (a - b = 3))) & (∀a ∈ A, ((∃b ∈ B, a × b = 7) ⇒ (∀b ∈ B, a + b ≠ 4)))) c) ¬((∃a ∈ A, ∀b ∈ B, ((a + b = 2) & (a - b = 2))) ∨ (∀a ∈ A, ((∃b ∈ B, a + b = 7) ⇒ (∀b ∈ B, a + b = 5)))) d) ¬((∀a ∈ A,((∃b ∈ B, a - b = 4) ∨ (∀b ∈ B, a + b ≠ 2))) & (∃a ∈ A, ∀b ∈ B, ((a+b = 5)∨(a−b = 5))))arrow_forward
- Determine if the following argument is valid or invalid. State if valid or invalid and the the law or fallacy used to support your answer. [(¬p → q) ∧ q] → ¬parrow_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_forwardb. ¬p ∧ q ∧ (q → (p ∨ r)) ⇒ r c. p → (q ∨ r)) ∧ ¬q ⋀ ¬r ⇒ ¬p solve useing Laws of logicarrow_forward
- What is the Truth value of the Expression ∀ (x)P(x) in each of the following interpretation? P(x) is the property that X is yellow, and the domain of interpretation is the collection of all buttercups. P(x) is the property that x is yellow, and the domain of interpretation is the collection of all flowers. P(x) is the property that x is plant, and the domain of interpretation is the collection of all flowers. P(x) is the property that x is either positive or negative , and the domain of interpretationarrow_forwardQuestion 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_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_forward
- Complete 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_forwardSimplify the following propositions using equivalence laws (B ∨ A) ∨ ¬B ∧ ¬(C ∧ ¬B) ¬(C → B) ∧ (C → B) ∧ ¬Barrow_forwardConstruct a truth table for (p ∨ ¬ q) ∨ (¬ p ∧ q) Use the truth table that you constructed in part 1 to determine the truth value of (p ∨¬q) ∨ (¬ p ∧ q), given that p is true and q is false. Determine whether the given statement is a tautology, contradiction, or contingency. p V (~p V q) ~ (p ∧ q) ~p V ~qarrow_forward
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