State h1 h2 S 3 3 A 3 C 2 1 3 2 E 4 4
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6. Consider the heuristics for this problem shown in the table above, h2 is admissible.
true or false?
The condition for heuristic is that the H1 should be less that or equal to the path from the H1 to goal node .
H1<=*(H2)
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Solved in 2 steps
- 3i need answer of all. if any answer will be skipped, your answer will be rejected. only complete answer will be accepted. b) Make a truth table for the statement ¬P ∧ (Q → P). What can youconclude about P and Q if you know the statement is true? a) Make a truth table for the statement (P ∨ Q) → (P ∧ Q). c) Make a truth table for the statement ¬P → (Q ∧ R).Part 1: Choose two of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the arguments. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. 1.(G • P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G • ~L) → K 2.(S v T) ↔ ~E, S → (F • ~G), A → W, T → ~W, therefore, (~E • A) → ~G 3.(S v T) v (U v W), therefore, (U v T) v (S v W) 4.~Q → (L → F), Q → ~A, F → B, L, therefore, ~A v B 5.~S → (F → L), F → (L → P), therefore, ~S → (F → P) Part 2: Below are basic arguments in English. Choose two arguments and translate those argument into the symbolism of predicate logic. You do not need to do a proof. Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul, Rx = x has a right to life). Some wars are just. No war of…
- 1. Prove by induction that Vi > 1, (L*)' = L*. • Basis: ? • Inductive Hypothesis: ? • Complete the rest of the proof: ?Exercise 1.4.4: Proving whether two logical expressions are equivalent. About Determine whether the following pairs of expressions are logically equivalent. Prove your answer. If the pair is logically equivalent, then use a truth table to prove your answer. (a) ¬(p ∨ ¬q) and ¬p ∧ q (b) ¬(p ∨ ¬q) and ¬p ∧ ¬q (c) p ∧ (p → q) and p → q (d) p ∧ (p → q) and p ∧ q3. Express the following English sentences using propositional functions, quantifiers and logical connections. (a) Someone in the class is helped by everyone in the class. (b) There is a hard working student in the class who has not been helped by any student in class. (c) For everyone in the class, someone who is smart has helped him/her. SO (d) There are two people in the class who have not helped each other. (e) There is a hard working student in the class who is helped by every smart student in class. (f) There are some companies that hire only hard working students.
- 7. Hany is a student in this class. He knows how to write programs in Python. Given that everyone who knows how to write programs in Python can get a high-paying job. Show that someone in this class can get a high-paying job using quantifiers and rules of inference.Consider the following true propositions:• p : The applicant has passed the learner permit test.• q : The applicant has passed the road test.• r : The applicant is allowed a driver’s license.For each of the following sentences write,symbolically, the compound proposition that correspondstothe given sentence in English asit is written (do not change the order or form of the expression).a) The applicant did not pass the road test but passed the learner permit test.b) If the applicant passes the learner permit test and the road test, then the applicant is allowed adriver’s license.c) Passing the learner permit test and the road test are necessary for being allowed a driver’slicense.d) The applicant passed either the learner permit test or the road test, but not both.e) It is not true that the applicant does not pass the road test and is allowed a driver’s license.Using predicate logic, prove that the following argument is valid. Provide the translation and the proof sequence. Every computer science student works harder than somebody, and everyone who works harder than any other person gets less sleep than that person. Riley is a computer science student. Therefore, Riley gets less sleep than someone else. Use the symbols, C(x), W(x,y), S(x,y), r.
- Exhibit the structure of the following statements by transforming them into a first-order formula,indicating the interpretation of predicates and the domain. For example the statement There isno greatest integer can be transformed into ¬∃x, ∀y, P(x, y) where P(x, y) is the predicate x ≥ y,the domain being the integers.Do not try to prove them (it may not be possible!).1. Every integer can be written as the sum of 2 squares.2. Every positive real number has a square root.3. The cosine function has zeroes.4. The cosine function has at least two distinct zeroes.5. There is a neutral element1for multiplication in real numbers.6. Every odd square can be written as the sum of three odd numbers.A fictitious setting, JUNGLE, is being described in PDDL terminology. There are three predicates in this universe, and each one may have a maximum of four arguments. There should be a limit on the number of JUNGLE states. It's important to provide an explanation.Write the following English statements using the following predicates and any needed quantifier. The domain of all variables are all at the school S(x): x is a student F(x): is a faculty member A(x, y): x has asked y a question Every student has asked Dr. Lee a question