Give a negation for “Vx3y(x> y)". Note that negation or NOT cannot be explicitly used in your answer. (15x)XAXA O (15XXAXE O (^ > XWAXA O O Vx3y(xsy) Let F(x,y) be the statement “x likes y" where the domain consists of all people in the world. (a). Use quantifiers to express "Not everyone likes Jack and Jill". (b). Give an equivalent statement of (a) using quantifiers.

Give a negation for “Vx3y(x> y)". Note that negation or NOT cannot be explicitly used in your answer. (15x)XAXA O (15XXAXE O (^ > XWAXA O O Vx3y(xsy) Let F(x,y) be the statement “x likes y" where the domain consists of all people in the world. (a). Use quantifiers to express "Not everyone likes Jack and Jill". (b). Give an equivalent statement of (a) using quantifiers.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Let L(X) be the statement " X visited London", let P(X) be the statement " X visited Paris" and let N(X) be the statement " X visited New York". Express the statement “None of your friends visited London, Paris and New York.” in terms of C(X), D(X), F(X), quantifiers, and logical connectives where the domain consists of all your friends.
Let I(x) be the statement "x has an Internet connection" and C(x, y) be the statement "x and y have chatted over the Internet," where the domain for the variables x and y consists of all students in your class. Use quantifiers to express each of these statements. i) Everyone in your class with an Internet connection has chatted over the Internet with at least one other student in your class. ii) Someone in your class has an Internet connection but has not chatted with anyone else in your class. Express each of these system specification using predicates, quantifiers and logical operators if necessary. i) There are at least two paths connecting every two distinct end points of the network. ii) No one knows the password of every user except for the system administrator who knows all password.
I. Let P (x) be the statement “2x = x2 .” If the domain consists of the integers, what are the truth values? a) P(0) b) P(1) c) P(2) d) P(−1) e) ∃x P(x) f ) ∀x P(x) 2. Let Q(x) be the statement “x > x - 1.” If the domain consists of all integers, what are the truth values? a) Q(10) b) Q(−2) c) Q(999) d) ∃x Q(x) e) ∀x Q(x) f) ∃x ˺Q(x) g) ∀x ˺Q(x)
Let S(x,y) be the statement "student x likes soft drink y" , where the domain for x consists of all students at your school and the domain for y consists of all soft drinks. Use quantifiers to express "Not every student likes tea and soda." 5.
: Let Q(x, y) be the statement “Student x has been a contestant on quiz show y”.Express each of the following sentences in terms of Q(x, y), quantifiers, and logical connectives,where the domain for x consists of all students at your school and the domain for y consists of allquiz shows on television.1. There is a student at your school who has been a contestant on a television quiz show.2. No student at your school has ever been a contestant on a television quiz show.3. There is a student at your school who has been a contestant on Jeopardy and on Wheel ofFortune.4. Every television quiz show has had a student from your school as a contestant.5. At least two students from your school have been contestants on Jeopardy.
Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.
QUESTION 5 Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The domain for x and y is the set of all persons. Write the negation in English starting by "Some .. " of : Vx 3y w(x) →R(y) ^ F(x,y)
Translate these statements into English, where C(x) is “x is a comedian” and F(x) is “x is funny” andthe domain consists of all people.a) ∀x(C(x) → F(x))b) ∀x(C(x) ∧ F(x))c) ∃x(C(x) → F(x))
Let P(x) denote the statement "x-3<12" where the domain consist of all non negative integers. Evaluate the truth value of 3xP(x)?
Problem 1: Let P(x, y) denote the statement “Student x has taken class y”, where the domain for x consists of all students in your class, and for y consists of all computer science courses at your school. Express each of the following quantifications in English.1. x y P(x, y)2. x y P(x, y)3. x y P(x, y)4. y x P(x, y)5. y x P(x, y)6. x y P(x, y)
9. Express the following statement ((P^¬R) → ¬(¬Q ✓ R)) in simplified V disjunctive normal form.
13. p(x): x is intelligent q(x): x reads book r(x): x is a student in your class Find the correct English translation for the following logical expression: ∀x(r(x)→(p(x) Λ q(x)) a. None b. There is an intelligent student in your class who reads book c. Every student in your class is intelligent and reads book d. All student in your class is intelligent and doesn't read book