Question 4. The following are logical laws shown in our lecture. Find their dual versions if exist. Implication law Idempotent lauw Commutative law A → B = ¬AV B ΑΛΑ Α АЛВ 3D ВЛА (АЛ В) ЛС %3 АЛ (ВЛС) АЛ (AV B) А Associative law Absorption law АЛ (BVC) (АЛ В)V (AЛС) Distributive law Double Negation law De Morgan's law Excluded middle law ¬A = A ¬(A ^ B) = ¬AV¬B A^¬A = F Identity law Domination law AAT = A ΑΛF F

Q: Determine which of the following statements are true, and which are false. Explain! (a) {a} ⊆ {a, b,…

A: Given that: (a)  a⊆{a, b, c}(b)  {a}⊆{{a,b},c}(c){a}⊆P{{a}, b, c}

Q: determine if the statements (pV ~ q) Λ (~ p V q) and (p → q) Λ (q → P) are logically equivalnet?

A:

Q: Select all that apply: Which of the following are equivalent to the statement "Nobody defeated…

A: Using the given symbol to select correct option equivalent to the statement ''Nobody defeated…

Q: On your work determine if p → (q → r) is logically equivalent to either of the following statements…

A:

Q: 3. Are the following logically equivalent? Explain why or why not. P - (Q v R) and (P→ Q) v (P→ R) म…

A:

Q: What kind of WFF is this? (Pv~Q) ~Q) = P V T FT TT TT TE TT F F FT T F FT TE F F a. contingent…

A: 28)Given that : P∨~Q≡P Truth table : P ∨ ~ Q ≡ P T T F T T T T T T F T T F F F T T F F T…

Q: A logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step.

A: The logical equivalence is,

Q: B is O A. P(Reject Ho | HA is true) O B. P(Fail to Reject Ho | Ho is true O C. P(Reject Ho I Ho is…

A: Given: β is provided

Q: If P (B) = 1/4, P (A ∪ B) = 1/2 and P (A|B) = 2/3, then which of the following statements is true?…

A: GivenP(B)=14P(A∪B)=12P(A|B)=23

Q: Question 1) B(x) means that " x has a car", T(x,y) means that "x and y talked on the phone", where…

A: If we have a sentence "∀x, P(x)" , then, its English translation is "For all x, P(x) is true". Also,…

Q: p=T, q= F, and r = T. Select the expression that evaluates to false. 1) (q^r) → p 2) (p^r) →q 3) (q…

A: Since, ,that is p is true, q is false and r is true.(1) So,   is F and negation of this is F,  (2)…

Q: Using De Morgan's law, which choice is logically equivalent to the following predicate statement:…

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Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: (2b) Let I = {2,4, 6, 8, 10} and S« = { a | a E I}. Prove or disprove the following statement: "If S…

A:

Q: 7. For each statement below, indicate whether the statement is true or false. {1} ⊂ (0,2) {1} ∈…

A:

Q: Simplify (-mvs)^-(mas) to ¬m 1. Select a law from the right to apply (-mvs)^-(mas)

A: We have ¬m∨s∧¬m∧s                       (1) By De Morgan's law ¬(a∧b)=(¬a∨¬b), we can write…

Q: Consider the proposed proof of the statement Proof Statement 1. VA, B, CCU,C- (AUB) = (A - C) U…

A: INTRODUCTION Similar to basic operations on integers, set operations are a notion. Mathematical sets…

Q: In ДАВС which of the following is FALSE? ) A. AB + BC + CẢ = 0 B. AB + BC – AC = 0 C. AB + BC – CẢ =…

A: Given triangle ABC,  To find the equation satisfying vector addition of sides.

Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B