Let P(x) be the statement "x can speak English", Q(x) be the statement "x knows thecomputer language C++" and R(x) be the statement "x is a good programmer". Express thefollowing clause in terms of P(x), Q(x) R(x), quantifiers, and logical connectives. The domainfor quantifiers consists of all students at your school."There is a student at your school if he knows C++ and he cannot speak Englishthen he knows C++ or he cannot speak English if and only if he is a goodprogrammer."

Discrete Mathematics is a part of the computer architecture that helps in understanding the laws and…

Answered: Let P(x) be the statement x can speak…

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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Form the negation of the following statements. Then apply De Morgan's law and/or conditional law, when applicable. Negation should appear only within predicates, i.e., no negation should be outside a quantifier or an expression involving logical connectives. Show all steps. a) Vx (P(x) A R(x)) b) Vy³z(-P(y)→→ Q(z)) c) 3x (P(x) V (VZ (R(z) →→Q(z))))
Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) D(x): x is a day S(x): x is sunny R(x): x is rainy M: Monday T: Tuesday 1. All animals are dogs. 2.Some animals are not cats. 3.Every animal that is a dog is not a cat. 4.Some animals are dogs and cats. 5.No animal is both a dog and a cat. 6. An animal is always a dog only if it is a cat. 7.No animals are dogs. 8.Meg is a cat; all animals are cats. 9.Meg and Alex are both cats. 10.If one animal is a cat, then every animal will be a cat.
Write the following English statements using the following predicates, anyneeded logical operators, and quantifiers if needed. Assume the domain of x is all students and thedomain of y is all states in US.B(x, y): Person x has been to state y. L(x, y): Person x likes state y. a. No one has been to every state in US.d. Alice has been to every state that Bob has been to.e. There is no state that both Alice and Bob have been to.
i need answer of all. if any answer will be skipped, your answer will be rejected. only complete answer will be accepted. b) Make a truth table for the statement ¬P ∧ (Q → P). What can youconclude about P and Q if you know the statement is true? a) Make a truth table for the statement (P ∨ Q) → (P ∧ Q). c) Make a truth table for the statement ¬P → (Q ∧ R).
2. Let P(x, y) be the statement "a2 6", where the domain for a consists of all integers between -4 and 4, and the domain for y consists of all real numbers. Determine the truth value of the following propositions. (a) 3avyP(x, y) (b) Væ3yP(x, y) (c) 3y(Q(y) A VæP(x, y)) (d) 3avy(Q(y) → P(x, y)) (e) Vy(3rP(r, y) → Q(y))
Mathematical Logic. First-order or predicate logic. For each of the following relations, give a formula that defines it in (N;+,∙). The language has equality and has the parameters ∀,+ and ∙. a) {0} b) {1} c) {〈m,n〉| n is the successor of m in N} d) {〈m,n〉| n<n in N} Please be as clear as possible. Thank you.
Develop a system/application in Prolog that will allow grader to: load a set of student’s grades (see samples from the Table C below) query student’s final letter grade (A, B, C, etc.) by a given student’s name. query student(s) whose grade matches to the input letter grade (e.g., A). For example, show student(s) whose final letter grade is A. There are 3 types of grades for each student—HWs, Exams, and Project, with a weight of 20%, 40% and 40%, respectively, to the 100-point final. Table A and B show how the final grades (in points and letter) are computed. Table C shows samples of students’ grades. You will define the execution instructions to answer the following questions so that grader can test out your application in Prolog: how to load your source code to Prolog runtime/compiler how to load students’ grades to Prolog runtime/compiler how to query student’s letter grade how to query student(s) whose letter grade matches to an input letter grade Please DO NOT hard code any…
Using the predicate symbols shown and the appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a bee. F(x): x is a flower. L(x, y): x loves y All bees love all flowers which one of these answer choices a. (∀x)(B(x) → [(∃y)(F(y) ∧ L(x, y)] b. (∀x)(B(x) → [(∀y)(F(y) ∧ L(x, y)] c. (∀x)(B(x) → [(∀y)(F(y) → L(x, y)] d. (∀x)(B(x) ∧ [(∃y)(F(y) → L(x, y)]
3. Formalize the following arguments in L1 providing a suitabledictionary. Make your formalization as detailed as possible. Ifyou find an ambiguity in the argument, explain it to justifyyour choice of formalization. (c) It’s not true that time travel is possible. For if I travelback in time and kill my grandfather, I will be born andunborn. But I will not be born and unborn. And I willtravel back in time and kill my grandfather, provided timetravel is possible.
(2) If ¬L is context free, then L must also be context free. True False

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