Question 3: Models of Computation (a) Are these propositional formulas satisfiable? (1) (pVg) ^ (r Vs) ^ (ii) (pv q) ^ (pV¬q) ^¬p (PV¬r)^(-qV¬s)^(PV¬s) Justify your answers. (b) If P NP, then such satisfiability questions can be decided in polynomial time. Briefly explain why. (c) Draw the reduction graph of the following term in A-calculus with arithmetic: (Ax.x+3)((Ay.y + 7)4)

Q: laws of logic to show that ((s VrV¬r) ^ (SV¬rva) ^ (rv¬sva)) = q v¬s.

A: The commutative law deals with the order of operations or the sequence in which elements are…

Q: what's the truth table(s) for (p=>q)≡((p∧¬q)=>F)? I think i'm getting confused with F being a…

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Q: Q2: Assume we have a robot in the Vacuum-world Problem which described in our lectures. If we extend…

A: Answer: I have given answered in the handwritten format in brief explanation

Q: We create the matrix "X" to solve a least-squares problem. Which of the following definitions of "X"…

A: The correct answer is Option 1 and Option 3   Explanation…

Q: Q4 Prove the following compound propositions by using a truth table. (a) (R ^ (R → S)) → S (b) (A ^…

A: Solution for the above question is given in step 2:-

Q: (*) Let p, q, r be propositions. Show that -[(p^q) v (p^ (-r)) V (qAr)] is logically equivalent to…

A: For the given question, we will be building truth tables for given expressions:  ~[(p^q)v(p^(~r)) v…

Q: hich of the following is NOT one of the axioms from XXV Y (XY) ⇒ [(Zv X) (Z V Y)] ⇒ XV X X

A: Solution - In the given question, we have to tell which is not the axioms from Hilbert's system.

Q: Question 3 (a) Show that [¬p v (p ^ q)] ^ ¬q → ¬(p v q) by using logical equivalence identities.

A:

Q: Simplify using the Logical Equivalence Laws or Algebra of Propositions 23. (P v ~Q) ^ (Q v ~S) ^ S…

A:

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Q: Show that the following issue belongs to the NP category: We are given a set S of integers and an…

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Q: ]To check if ¬(p∨q)¬(p∨q) and ¬p∧¬q¬p∧¬q are logically equivalent? 2] A truth table for…

A: Step 1  The answer is given in the below step

Q: Simplify ¬(s^(qv¬s)) to ¬sv¬q

A: In step 2. I have provided complete answer to the question....

Q: change b1,b2,… ,bn permits a stretch [l′,r′] to holds its shape if for any pair of integers (x,y)…

A: Here have to determine about the sort out all k-comparable changes problem statement.

Q: Briefly explain how the following tautologies may be used in the method of proof by contradiction:…

A: According to the given question   (~p  implies  (q ^~q)) implies p.

Q: (sv ((b^l) ←d)) v ((1² v d) ← s) ! 1. ((p^¬q) → (q ^r)) → (s V¬q) i. (db) v (b←d) (1 Mark) (1 Mark)

A:

Q: 2. Using a truth table, show whether the following wffs are satisfiable. B. justification for your…

A: A compound proposition is said to be satisfiable if it is true for some of truth values to its…

Q: Show that the following issue belongs to the NP category: We are given a set S of integers and an…

A: The given issue belongs to the NP (nondeterministic polynomial time) category because:

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A: Writing it below

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A: Given Data : (i) (P→Q), (Q→R) ⊨ (¬R→¬P) (ii) (P∧Q)∨(P∧R), (Q∧P)→R ⊨ (R∨P) <->Q

Q: B= (b1,b2,...,bn). Let I, be the set of integers: {1,2,...,n}. Make a formal assertion for each of…

A:

Q: Part V Construct a formal proof of validity for each of the following using CP and/or RAA. A) 1. A→…

A:

Q: Is (((Væ)(A → (B → C))) = ((r)A) ^ (B → C))) an absolute theorem schema?

A: ABSOLUTE THEOREM :It says if the equation is valid or not.

Q: - universal generalization (twice-applied) that (((C − A) n B) u (D n B)) = (B n ((C − A) U D)).

A: Answers:- To prove that (((C - A) n B) U (D n B)) = (B n ((C – A) U D)) using universal…

Q: Show that: ¬q 1) p→¬q 2) (p∧r)∨s 3) s→(t∨u) 4) ¬t∧¬u   where ¬ is denied.

A: Discrete Mathematics which refers to the one it is the study of mathematical structures that deal…

Q: Construct a formal proof of validity for the argument. -(a^(byc)) → ~(~d^(a v (byc)/NTS (need to…

A: Given argument is, ~(a∧(b∨c))→~(~d∧(a∨(b∨c))) The variables present in the given argument are a, b,…

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

A:

Q: Simplify using the Logical Equivalence Laws or Algebra of Propositions 21. (~(P ^ S) v ~Q) ^ (P v…

A: The answer is given below.

Q: f(x) = = xxx Show that f is a total computable function by 1. Providing a high-level description of…

A: Answer:Introduction:1) Given Σ={0} and f : Σ + -> Σ +2) Given the function as f(x) = x.x.x.3)…

Q: A discrete-time system can be (Static or dynamic, Linear or nonlinear, Time invariant or time…

A: A discrete time system is anything that takes a discrete time signal as input and produces a…

Q: Prove that the following argument is valid. a is an element in the domain. Væ(P(x)V Q(x)) ¬P(a) ..…

A:

Q: Given the predicate expressions in Horn Form, use Backward Chaining to determine if Sam is at the…

A: Backward chaining is a type of inference algorithm used in artificial intelligence and expert…

Q: Complete the logical proof for the following argument. ExP(x) X(P(x) → Q(x)) : 3xQ(x) Justification…

A: Here we have given 2 premises and one conclusion in predicate calculus. Premise 1 ∃x P(x) There…

Q: the following formal theorems: (a) E (p = 4) = (¬9 v e6)

A: 4.  Let co, E S(P). Give derivations (Using Equational Layout)) of the following formal theorems:…

Q: in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak}…

A: ProofTo show that the set M, characterized by the axiom framework {F1, F2, F3, ...}, where every…

Q: QUESTION 4 Which of the following is a negation of the statement ((X)O^(X) dL)XA ((X)0L V (X)d)XA…

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Q: Simplify the following using the algebra of propositions. Justify each step with the law you used.

A: lets take as P , the Z becomes  By associativity we can write by and-simplification we can write…

Q: 4. Let y, ý E S(P). Give derivations (Using Equational Layout)) of the following formal theorems:…

A:

Q: Construct the truth (tables) values of the given compound proposition: [(p^q'Ar) + (p O q)] – [(p' &…

A: XOR is represented by ⊕. AND is represented by ∧. OR is represented by ∨. ↔ represents…