In the image is predicate proofs. I am to prove the validity of the arguement using the quantifier rules and rules of inference and replacement The following 4 arguments are valid. Provide a proof of validity for each argument. You can use the 18rules of inference, CP, IP, the rules for introducing and removing quantifiers and the Change of Quantifierrules. Questions #23 and #24 are more challenging, they involve relational predicates, overlappingquantifiers, and identity.22.1)2)23.1)24.1)2)(3x) Ex (3x) (Gx. Hx)(3x) HX= (x) JX- (x) (Ex - Jx)(3x) [Lx. (y) (My = Pxx)]~bb(x) [Hx (Lx.x = b)]/:. (3x) [Lx. (Mb⇒ P.xb)]7:. ~ Ha

Since you have posted a multiple question according to guildlines I will solve first (Q22)question…

Answered: The following 4 arguments are valid.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Justify each conclusion with a derivation rule. (a) If Joe is artistic, he must also be creative. Joe is not creative. Therefore, Joe is not artistic. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification (b) Lingli is both athletic and intelligent. Therefore, Lingli is athletic. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification (c) If Monique is 18 years old, then she may vote. Monique is 18 years old. Therefore, Monique may vote. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification (d) Marianne has never been north of Saskatoon or south of Santo Domingo. In other words, she has never been north of Saskatoon and she has never been south of Santo Domingo. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification
Translate into symbolic form and check for validity of the following argument: • No good car is cheap • An Omnex is not a good car. Therefore, An Omnex is cheap.
Give a truth–table proof to tautology((¬q⇒¬p)Λp) =⇒q
Construct a formal proof of validity for the following symbolized argument. 1. (∀zHz&∀xLx), ((La&Ha) →∃x(Dx&Ax)), (∀xLx →∀zRz), ├ (Ra&∃xDx)
Use the rules of inference, show that the given argument is valid or not. The domain is all persons. "You are listening, and I am speaking. If you are listening, then it is not silence. If music system is off then it is silence. If music system is not off then we are in happy mood, imply the conclusion that we are in happy mood and we are good friends.". Give a reason for each step of proof.
We have said what it means for a formula F to be: (1) a tautology, (2) contradictory. That F is a tautology and that G is contradictory represent two extreme poles of the spectrum of truth values for formulas in sentential logic. Most formulas involving sentences in English are neither tautologies nor contradictory. So, call a formula F satisfiable or contingent if its truth function has value 1 under at least one truth value assignment to its component simple sentences. It follows that a formula F is unsatisfiable if its truth function has value 0 under every truth value assignment to its component simple sentences. Your task is to use truth tables to determine whether the following formulas are: tautologies, contradictory (unsatisfiable) or contingent (satisfiable). (f) (¬¬p → p) (g) (p ∧ ¬p) (h) (p → (q → p)) (i) ((p ∧ q) ∧ (¬p ∨ ¬q)) (j) ((p ∨ q) → (¬p ∧ ¬q))
Discrete Mathmetics 2015 Review for Test 1 1. Determine whether the following propositions are T or F a) 2+1 = 4 or 4+3 = 6 b) 4+5 = 8 or 2+5 = 7 c) 8-5 = and 3 6 = 9 d) 5+6 = 10 and 2+3 =6 2. Determine the truth values of the following statements. If False, give a counter- example. Suppose the domain = {1,2,3,4} a) Vx (x+3<6) b) 3x (x+<6) 3. Let p: I go to Delhi Q: I visit Red Fort R:I visit Rajghat Which propositions for the following sentences using symbols. a) If I go to Delhi, then I visit Red Fort b) I go to the Delhi, but I do not visit Red Fort. c) Either I visit Red Fort it I visit Rajghat. d) Neither do I visit Red Fort, nor do I visit Rajghat. e) I go to Delhi, and I visit Rajghat, but I do not Red Fort. f) If I go to Delhi, and do not visit Red Fort, then to Delhi. g) To visit Delhi Red Fort, it is necessary that I go to Delhi. h) I go to Delhi if and only if I visit Red Fort and Rajghat. i) To visit Red Fort and Rajghat, it is sufficient for me to go to Delhi.
For the second picture I only need numbers #11 and #13 to be done For each proof, you must include (i.e., write) the premises in that proof. I do not want to see any proofs without premises. Do not use any transformation rules (e.g. contraposition) in your proof other than DN. Only use the eight inference rules. YOU CANNOT USE CONDITIONAL PROOF (CP), INDIRECT PROOF (IP), OR ASSUMED PREMISES (AP).
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Are the statements ¬(p>q) and ¬p- ¬g logically equivalent? O True O False
Give a truth–table proof to tautology((¬q⇒¬p)Λp) =⇒q
In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates: • P(z) : z was given the placebo • D(z) : z was given the medication • M(z): z had migraines Translate cach of the following statements into a logical expression. Then negate the expression by adding a negation operation to the beginning of the expression. Apply De Morgan's law until cach negation operation applices directly to a predicate and then translate the logical expression back into English. Sample question: Some patient was given the placebo and the medication. 3r (P(z) ^ D(z)) • Negation: ¬ar (P(z) ^ D(z)) Applying De Morgan's law: ¥z (¬P(z) V ¬D(z)) English: Every patient was either not given the placebo or not given the medication (or both).

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