Consider the following knowledge base Prove that Q is true with: 1. P → Q 2. L ∧ M → P 3. B ∧ L → M 4. A ∧ P → L 5. A ∧ B → L 6. A 7. B Forward-Chaining Backward-Chaining Resolution Prove t → s: 1. p → q 2. [q ∧ r] → s 3. [t ∧ u] → r 4. u → w 5. t → y 6. y → u 7. r → p 8. p → m i. Express in clause form ii. Forward-Chaining iii. Backward-Chaining iv. Resolution

Q: Consider the language that contains the predicates of symbols degree, student, pass, test,…

A: Introduction Propositional language: Propositional language is a type of formal language used in…

Q: a. L= {x€{a, b, c }* | na(x) < n»(x) and na(x) < nc(x) }, where n(x) is the number of occurrences of…

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Q: 1.a Using a Cross Product method, construct a minimal DFA of w ∑ (a, b) *, where Number of 'a' in a…

A: a) Given that, Set of input alphabets= {a, b} where Number of 'a' in a string w mod 2=0 and number…

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Q: Prove the following consequent in natural deduction:

A: Proved the given consequent in natural deduction

Q: (3) {w € [0, 1]*: w has 001 as a substring} Testing strings: €, 0, 1, 01, 000, 001, 0001, 0010,…

A: We are given a language {w ∈ {0,1}*: w has 001 as a substring}.And we are asked to test given…

Q: S PP VP VP VP VP P ↑ NP VP P NP VP NP VP PP types program with 1.0 1.0 0.3 0.3 0.15 0.25 1.0 NP →>>…

A: Using above pcfg and the rule there are two best and suitable parse trees are possible which holds…

Q: Using resolution and proving by contradiction/refutation that "¬Cat(Sister)" is entailed by the…

A: Here is the explanation regrading the proof "¬Cat(Sister)" is entailed by the knowledge base.

Q: Given the grammar    F>   GnF | mZpG G    >    pZ | mZpM | q    Z    >    mG | mGp | m…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Question 5. Recall that EQCFG = {(G, H) | G, H are CFGs and L(G) = L(H)}. Show that EQCFG is…

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Q: For each statement below, decide whether it is true or false. If it is true, justify your answer. If…

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Q: Question 3. Consider the language L = {w€ {0, 1}* | the strings 01 and 10 occur the same number of…

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Q: Using predicate logic, prove the following argument. (Hint: The deductionmethod still…

A: The following inference rules will be used to prove the given argument: Modes ponens: |P → Q|  Λ…

Q: Given: ∀x [p(x) → q(x)] ∀x[p(x) → (∀y w(y))] ∀x ∀y [(q(x) ∧ w(y)) → s(x)] p(MARY) Show s(MARY)…

A: The answer is as follows.

Q: Think about the concept of extended transition functions δ* and ∆* of Deterministic Finite Automata…

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Q: (I) State the pumping lemma with all its conditions and indicate how you go abou proving that a…

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Q: The proposition p q is logically equivalent to a. [(NOT q> NOT p) AND (q -> p)]. -> O b. [(p > NOT…

A: pq~p~qp↔q∼q→∼pq→∼p∼q→∼p &amp; q→∼pTTFFTTTTTFFTFFTFFTTFFTFFFFTTTTFTclearly option A is correct.

Q: | Design a non-deterministic push down automaton (NPDA) N = (Q, {x, y, z, w}, {1, a}, 6, s, I, F)…

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Q: (4) {w € [0, 1]* : w does not have 001 as a substring} Testing strings: €, 0, 1, 01, 000, 001, 0001,…

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Q: A set S of logical connectives is said to be (logically) complete if each of ¬,∨, and ∧ can be…

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Q: Prove that r V (¬r → p) is a tautology by applying the laws of propositional logic. Enclose math…

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Q: Consider the language L on = {0,1} with L={w] w has an even number of 0's and ends with 1 } 1. Find…

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Q: Let A be mapping reducible to B (A Sm B). Which of the following are true (circle them). a) If B is…

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Q: 4. Using equivalences previously proven in the lectures, prove the following logical equivalences…

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Q: Q2. Determine whether each of these statements is true or false. x ∈ {x} {x} ⊆ {x} {x} ∈ {x} ∅…

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Q: Construct a DFA that accept the language, L = { w€ {a,b): w starts and ends with different symbols.}…

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Q: 6. Prove or disprove that the two propositions in each pair are equivalent. a) (p→ (q → r)),…

A: Task : Given the expression. The task is to check if these expression are equal or not.

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Q: Decide whether each statement is true or false. If it is true, justify your answer. If it is not…

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A: ANSWER: X closed paths:

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Predicates

A predicate is a function defined with set of variables, which returns the result True or False. The output of a predicate is a Boolean value as a response when given a set of parameters: