Consider the wffs: φ1φ1 = p1→→(p2→→(p3→→p4)) φ2φ2 = (p1 ^ p2 ^p3)→→p4 φ1 ≡ p1 ∨ ¬p2 ∨ p3 ∨ p4 φ2 ≡ ¬p2 → p3 φ3 ≡ p1 → p3 φ4 ≡ p3 → (p2 ∨ p4) φ5 ≡ p3 → p4 φ6 ≡ p3 ∨ ¬p4 φ7 ≡ p4 Show using resolution that (φ1 ∧ φ2 ∧ φ3 ∧ φ4 ∧ φ5 ∧ φ6) → φ7 is valid.

Q: Consider the following P = {P1, P2, P3, P4, P5) R = (R1, R2, R3, R4) E = {P3 R1, P2R2, R4P4, R2→P1,…

A: Given that, P = {P1, P2, P3, P4, P5} R = {R1, R2, R3, R4} E = { P3→R1, P2→R2, R4 →P4, R2→P1, P5→R3,…

Q: Construct a truth table to show if (p → q) ^ (p → r) and p (q A r) are logiclly equivalent. p → q p…

A: Truth table for implication:                                                                   A…

Q: use semantic tableaux to show that ¬ (p^¬q) 7 Vr,p>(r=s) p=q is invalid

A: Answer :-

Q: Complete the following truth tables:

A: Required Truth table is given below

Q: ¬[[p → ¬q) v s] = [p Aq A -s] -[[p → ¬q) → s] = [¬(p^q) A¬s] [(pA¬q) → s] = [¬s → (-p v q)] [¬s →…

A:

Q: P = {P1, P2, P3, P4, P5) R = (R1, R2, R3, R4) E = {P3 R1, P2-R2, R4→P4, R2-P1, P5-R3, P3-→R4, R1→P3,…

A: Given that, there are 5 processes that are P1, P2, P3, P4, P5 and four resources that are R1, R2,…

Q: Consider the following P = (P1, P2, P3, P4, P5) R=(R1, R2, R3, R4) E = {P3 R1, P2R2, R4P4, R2P1,…

A: The Answer start from step-2.

Q: Assuming that Σ = {0, 1}, for the expressions given below, draw transition diagrams and transition…

A: Assuming that Σ = {0, 1}, for the expressions given below, draw transition diagrams and transition…

Q: p>q = (p→q)^(q → P) p>q =¬p+¬q p+q = (p^g)v(¬p^-9) G(p+q) = p+¬9

A: A) (p<->q) ≡ ((p->q)∧(q->p))   (p<->q)   P q p<->q T T T T F F F T…

Q: Convert the binary number 111010101.110111 to hexadecimal.

A: In question 1, we have given binary number and we have to convert it into a hexadecimal number. As…

Q: S > aA S → BA ВА A → Sb A a B → bB → cDc → AB

A: Given : S -> aA S -> BA A -> Sb A -> a B -> bB B -> b C -> cDc D -> AB

Q: To disprove a conjecture you need only find one case or counter-example - where it is not true.…

A: Given Data: Y =  [( p∧q )→r]↔[( p→r )∧( q→r )] .

Q: Determine the value of the following formula under the interpretation v(p) = T, v(g) = F, v(r) = T:…

A: Given, v(p) = T v(q) = F and v(r) = T   We have to find the value of the formula…

Q: Which of the following best describes the transition function of a nondeterministic PDA? Note: Σ and…

A: Option C is correct answer

Q: For the two chains of number sets given here, derive a rule for moving along an arrow, and a rule…

A: Given two chains are, {57,36}→{21,36}→{21,15}→{6,15}→{6,9}→{6,3}→{3,3}={3} stop…

Q: Consider the following P = (P1, P2, P3, P4, P5} R = (R1, R2, R3, R4} E = {P3 R1, P2R2, R4P4, R2 P1,…

A: The Answer start from step-2.

Q: 1. Which of the following are tautologies, contradictions, or contingents? a) - (pAq) (-p) v (- q)…

A:

Q: logiclly equivalent.

A: ANSWER: Logically Equivalent: The refutation of a restrictive assertion can be written as a…

Q: Consider the following P = {P1, P2, P3, P4, P5} R = (R1, R2, R3, R4} E = {P3 R1, P2R2, R4P4, R2P1,…

A: ANSWER:

Q: 1. Consider the formula A = (Vx pi(x, a1)) → (3y (p2(y) p3(y, a2)) ^ (a) Create a formula tree for…

A: (a) The formula tree for A is:

Q: Please explain in detail Use semantic tableaux to prove or disprove the following entailment: а: [p…

A: a: [p→ (¬h → c)]^(p → ¬h) ‡ p → c b: (p^q) →r ‡  (p →r) V (q→r)

Q: Solve for the DNF and CNF of the following: 1. 1. ¬ (q → p) ∨ (p → r)

A: A propositional formula is in disjunctive normal form (DNF) if it a disjunction of conjunctions. It…

Q: Simplify and show solution. A. [¬p ^ (p ν q)] → q B. (p → q) ↔ (¬p ∨ q) C. [(p → q) ^ (q → r)] →…

A: Boolean laws and equivalences to simplify : 1) p^(q ν r) =  (p^q) ν (p^r)    //distribution 2) p → q…

Q: Consider the alphabet {a-z, A-Z, 0-9, -, E} and the following regular defi note the first - is the…

A: Given Regular definitions are: SUM->(-|+)?[0-9]2(E [0-9]+)? SID->[A-Z][a-z]*…

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

A: The first question asks to find the negative of the first-order logic & the second question asks…