Answer each of the following questions. [No explanations required.](a)What is the shortest formula in sentential logic that is tautologically equivalent to '(P v -P) ^ (Q v Q)'?(b) Find a formula in sentential logic that is tautologically equivalent to 'PA¬Q' but does not contain ^'.(c)Find a wff in FOL that is logically equivalent to 3x(a v B)' but contains neither 3' nor 'v'.(d) Find a wff in FOL that is logically-but not tautologically implied by 'a = b'.(e)Find a wff in FOL that is logically-but not tautologically-implied by 'F(a)'.(f)Give an instance of wff in FOL with quantifiers that is not a sentence.Answer to (a):Answer to (b):Answer to (c):Answer to (d):Answer to (e):Answer to (f):

Note- As per guidelines answering first three parts. a) Hence the shortest formula is Q.

Answered: Answer each of the following questions.…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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I need help to answer Question no. 30 prove that the below WFF is a valid argument. (∀x)(∀y)[(P(x) Λ S(x,y)) →Q(y)] Λ (∃x)B(x) Λ (∀x)(B(x) → P(x)) Λ (∀x)(∃y)S(x,y) → (∃x)Q(x) Chapter 1.4 - Predicate Logic Text Book: Discrete Mathematics and its application 7th edition. Author: Judith L Gersting.
1. Explain the difference between first-order logic and propositional logic. 2. The language of first-order logic is based on objects and relations. An example of a first-order logic expression is "squares near the WAMPUS are smelly." What are the objects and relations in that expression? 3. What is an atomic sentence? Give an example. 4. What is the universal quantifier? Write the sentence "All kings are persons" using the universal quantifier and other logic symbols. Hint: To find the logic symbols in blackboard click on fx from the toolbar above and select the symbols tab. 5. What is the existential quantifier? Write the sentence "There is a prime number that is even" using the existential quantifier and other logic symbols.
(a) Is it possible for an argument to be sound and have a false conclusion? Explainyour answer (in one or two sentences).(b) Is it possible for an argument to be invalid and have a true conclusion? Explainyour answer (in one or two sentences).(c) Explain what a tautology is.(d) Explain what semantic entailment is.(e) State the deduction theorem.(f) If A ⊨ B, then A, C ⊨ B. What is this feature of entailment known as?
(b) Let C(x, y) mean that "student x has taken course y", where the domain for x consists of all students at your school and the domain for y consists of all courses offered at the university. Express each of these sentences in terms of C(x, y), quantifiers, and logical connectives. (i) Not every student has taken the course SWEN2002. (ii) Laila has taken every course except for SWEN3000. (iii)Kayley has taken exactly one course. (c) Write each of the following statements in the form if p, then q. (i) Shane has an allergy whenever he eats peanuts. (ii) It is necessary to have studied abroad to have the full experience of university. (iii)Rich will yell unless the children do not walk on his lawn. (d) Given the hypotheses, mk and (-h A-k)→ -p, m A p show that-h→m is a valid conclusion.
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The following sentence is a theorem of truth functional logic. (P → (Q → (P ∧ Q))) (a) Explain in a sentence how to use a natural deduction proof to show that a sentence of TFL is a theorem (1 point). (b) Using any of the proof rules (from Ch. 16 & 18 of the text) in the natural deduction system, complete a proof that shows that this sentence is a theorem
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Translate each of these nested quantifications into an English statement that expresses a mathematicalfact. The domain in each case consists of all real numbers.a) ∃x∀y(x + y = y) b) ∀x∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0))c) ∃x∃y(((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0))d) ∀x∀y((x ≠ 0) ∧ (y ≠ 0) ↔ (xy ≠ 0))

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