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: 1.2. Verify that the analytic solution of the differential equation in 1.1 above is y = e**- and…

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Q: (¬AUB→(CND))(¬AUB→(CND)) ¬AUB→CND¬AUB→CND (¬AUB)→(CND)(¬AUB)→(CND) ¬AU(B→C)ND they saying the same…

A: We have to show the following expressions are equivalent or not 1. (¬A∪B→(C∩D))2. ¬A∪B→C∩D3.…

Q: Which of the following expressions is NOT equivalent to ((Y \ (Z \ Z)) \ (X UY))? (Please note -…

A: Given, the expression                                We have to check that which one gives the same…

Q: c) not a tautology. pV ¬q (pV ¬q) → q True True False True True True False True True False False…

A:

Q: R→T T :. P ¬Q) → (RAS) 1 2 3 4 5 7 8 9 STATEMENT R→ T (¬PV ¬Q) → (RAS) ¬RV¬S ¬¬PV¬Q) REASON…

A: I shall solve in details in next step

Q: 1.3x)(P(x)→Q(x)) and Vx(Px)→3xQ(x) are logically equivalent true or false

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Determine the validity of the ff. argument: ( Note: "-" means "-") a. b. С. d. u V w f. ..~t е. O…

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Q: Let C(x, y) = "Student x is enrolled in course y. %3D Which choice below expresses the following…

A: let Cx,y="student x is enrolled in cource y given an expression ∃x∃y∃z x≠y∧Cx,z→Cy,z claim- to check…

Q: Question 5) Prove that the following expression whether tautology or not using logical expressions?…

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

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Q: s it the case tha your answer.

A: a) φ→ψ Here, ω=tatology

Q: 4 -1 01 If A = В 1 3- А. В 3 11 2

A:

Q: Simplify WAT to w 1. Select a law from the right to apply ¬¬WAT Distributive (a^b)v(a^c) = a^(bvc)…

A: Here we firstly apply double negation law and then identity law.

Q: If A and B are two equivalent sentences, then (a) A → [(A v B) Ð~ B] is true (b) A → [(A v B) O~ B]…

A: The truth table for A→B can be presented as follows. A B A→B T T T T F F F T T F F T…

Q: Supply a reason for each step in the solution below showing ((p→ q) → plp is a tautology. [(p - q) -…

A: We have to solve given problem:

Q: QUESTION 1 Which is the contrapositive of "If March comes in like a lion, it goes out like a lamb"?…

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Q: De Morgan's Laws: ~(A/B) ~AV~B ~(A V B) ~AA~B Given the statement, rewrite using De Morgan's Laws,…

A:

Q: Consider the following statement: 3x, y, x+y= y. From the options provided below, which universal…

A: Given statement  , x+y = y  So it means there exist x such that for all y x + y = y x = 0

Q: Given: 5x+4y= 24, x + 7y= 11; Prove: y = 1

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Q: السؤال 5 0 صواب 0 خطأ السؤال 6 (2-i)(5+3i) = %3D 7+2i o 3+4i O 14i O 13+iO

A: 5) The given inequality is z1-z2≥z1-z2. Triangle inequality: If z1 and z2 are complex numbers, then…

Q: Values for A, B, and C are true and X, Y, and Z be false. ~[~[(CV~B)-(ZV~A)]-~[~(BVY)·(~XV)]]…

A: C∨~B=T∨~T=T∨F=TZ∨~A=F∨~T=F∨F=FB∨Y=T∨F=T~X∨Z=~F∨F=T∨F=T

Q: ged Carb) =d Then la dlb adl ar. True or false

A:

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: Let M(x, y) be the statement "x is a role model for y," where the domain for both x and y consists…

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Q: Determine if the following statements are logically equivalent. Ensure that you explain the steps…

A:

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.

A:

Q: 1) State the name of the law used in the identity: i. -(-p^q) V T=T ii. TV¬(¬p^q) =¬(¬p^q) V T, iii.…

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

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

A:

Q: (a) Give a logical expression using only - and A operators which is equivalent to the expression P=…

A: formula:

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: Boolean Algebra Practice Problems: Simplify each expression by algebraic manipulation. 1) a+0= 2) a…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first three parts of…

Q: 1)dependent or independent 2) dependent or independent 3) dependent or independent

A: Given,P(A)=15 ,  P(B)=310  ,   P(A and B)=3100