Show that [(p ∨ q) ∧ (p => r) ∧ (q => r)] => r is a tautolgy

Q: Suppose that A ⊆ B and x ∈ A. Use the method of “proof by contrapositive” to show that if x ∉ B - C,…

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Q: The Boolean sum of the variables z, y and z or their complements, that has the value 0 if and only…

A: Given x=0y=1z=1 Thus yc = 0zc = 0 We know that  a+b = 0 if and only if both a and b are zero

Q: Let Q(x, y) be the statement "student x has been a contestant on quiz show y." Express "At least two…

A: The statement is "Atleast two students from your school have been contestants on Jeopardy" x :…

Q: study of pain relievers,  100  people were given product A, and  75  experienced relief. In the same…

A: Let  x denote the expereinced relief with product A. Let n1 denote the number of pain relievers.…

Q: 5. Show that (¬ p V q) → ((p ^ ¬q) is a tautology.

A: Question 5 is wrong, two modifications possible: Either write contradiction in place of Tautology or…

Q: Show the output of a Universal and Existential quantification of the given fu 1.3XQ(x): x sx+2 Q(x)…

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Q: Let P, Q, and R denote the propositional variables. Prove that the following well-formed formulas…

A: We know that P is True if and only if ¬P is False P∨Q is False if and only if both P and Q are False…

Q: Consider the statement: For all r, y, z E Z. At least one of x– y, I – z and y – z is even. (i)…

A: For all x,y,z ∈Z, Road map: 1.Let's suppose x-y, y-z,x-z are odd . 2.If we prove that atleast one of…

Q: What rule of inference has two variants where the first points out that either P and Q are both true…

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Q: Construct a Boolean expression having the given table as its truth table. PQRS 1 1 1 0 1 0 1 1 10 10…

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Q: What is the contrapositive of the followir (NV-0) M M →((NAO) (-NAO) O-MyN) (-M VN) GN VONH> M M…

A: Given statement is N∨¬O→M. The given statement means that the expression N and negation of O…

Q: Let (M) be the statement: "It will stay whenever it is for our good". The contrapositive of (M) is

A: Since the contrapositive of a statement of form 'if p then q' is of form 'if ~q then ~p '

Q: The disjunction of three sentences is false O if and only if at least one of the sentences is false.…

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Q: Let P(x) be a property about some object x of type X. If we want to disprove the claim that "P(x) is…

A: Given that : Let P(x) be a property about some object x of type X. And the claim is " P(x) is true…

Q: Show that the statement (V P(x)) V (Vx Q(x)) → Vx (P(x) V Q(x)) is a tautology. Show that its…

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Q: Show, by the use of the truth table/matrix, that the statement (pvq)v [(¬p)^ (¬q)] is a tautology.

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Q: Prove using the sequent calculus that (pAq) V-p V ¬g is a tautology.

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Q: Show that [(p∨q)∧(p→r)∧(q→r)]→r is a tautology

A: To Show that [(p∨q)∧(p→r)∧(q→r)]→r is a tautology I will prove by using truth table method and rules…

Q: Prove that the statements ∀x∀yP(x,y) and ∀x∀yP(y,x) are logically equivalent .

A: Given statement is ∀x∀yP(x,y)  and   ∀x∀yP(y,x)   are logically equivalent . We have to prove that…

Q: If n is not a poime then there exist Some ab€ 7h Such that ab # Itnk fox all

A: Definition: A number which can not be factored as product of two numbers other than the number…

Q: 1. Show that the following language is decidable, by reducing it to ECFG (which we already know is…

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Q: Prove or disprove using the replacement rules that each of the following statement is a tautology.…

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Q: 1. Show that -(p v q) and -pA-q are logically equivalent.

A: # We are entitled to solve one question at a time ,please resubmit the other question if you wish to…

Q: 3. Show that the statement p V ¬p is a tautology.

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Q: A is a tautology if and only if NotA is unsatisfiable. Prove

A: Some definitions: Definition 1: A (truth) valuation is a function v that assigns truth values. For…

Q: Prove by resolution that "John likes peanuts" if you have these sentences in the knowledge base: -…

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Q: Let A = {a} and B = {{a}}. Prove that in general A + B. Thus, the presence of curly brackets is…

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Q: In a recent study, 100 males used a new weight-loss supplement, and all but 29 of them experienced…

A: The percentages of males and females not experiencing weight loss is calculated. Percentage of…

Q: What rule of inference has two variants where the first points out that either P and Q are both true…

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Q: Show that the statement (Væ P(x)) V (Væ Q(x)) → Vx (P(x) V Q(x)) is a tautology. Show that its…

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Q: Prove that there are compound statements that are not equivalent to any statement using only the…

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Q: Is (p ^ q) → (p V r) a tautology? Prove or disprove it.

A: We will check whether the given statement is true or false.

Q: 8. Show that ¬(p → q) V (-p + ¬q) is a tautology.

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Q: A discrete mathematics class contains 1 mathematics major who is a freshman (1st year), 12…

A: Let, Mx: x is a mathematics major. Cx: x is a computer science major. Jx: x is a junior. Sopx: x is…

Q: an be cauchy, prove why a subsequence of (an) must also be cauchy.

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Q: 1. Show, by the use of the truth table/matrix, that the statement (pvq)v [(¬p)^ (¬q)] is a…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1) Find the "axa"-netrik A such that, » A(;)- () ) A(;)- (3) o) A (*)- (:) «) A (;) - (*) 4) (*-yo A…

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Q: R is commutative if and only if R[x] is Commutative. True or False

A: The given statement is true. If Rx is cummutative.So, R⊂RxRx is cummutative.R is also…

Q: 2.Show that (P 'n Q) V (Q 'n P) is a Tautology.

A: To Show- Show that P' ∧ Q ∨ Q' ∧ P is a Tautology.

Q: (e) The proof of Theorem 1 is thus currently incomplete, as it does not explicitly use the…

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Q: Question 8. A Compound proposition that is neither a tautology nor a contradiction is called.. . A.…

A: Definition of Contingency: A compound proposition that is always true for all possible truth values…

Q: 10. Prove: A and B countable > Ax B countable.

A: According to the given information, Let A and B be two countable sets then it is required to prove…

Q: or disprove IOwing statei ient: If > an and > bn are both divergent then )(an + bn) is divergent.…

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Q: Show that the proposition ((p → q) ^ (q → r)) → (p –→r) is a tautology.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Use the rules of inference to show that if 3x(M(x) ^ P(x)) and Vx(K(x) → ¬M(x)) are true, then…

A: Introduction: When an argument is given in quantified form, the rules of inference are also used.…

Q: Exercise 15. Use the method of conditional proof to explain in words why the sentence {(Pv Q)A [(P=…

A: Given: P∨Q∧P⇒R∧Q⇒S⇒R∨S To find: Tautology

Q: Evaluate (~p a p) → ~q using the table belov O FFFT O Self-contradiction O Tautology FTFT O FFTF

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Q: If R is reflexive, then R is reflexive. O True O False

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Q: a) Show that (a V b → c) → (a ^ b → c) is a tautology but its converse is

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.