1. Let G(x, y) denote that x gets y; W(x, y) denote that x wants y, and P(x) denote that x is a person. Match the following sentences with their equivalent sentence of predicate logic: a. If everyone wants something, then no one gets it. b. Some people want only things they don't get. c. There is something that nobody wants. 1. Ex: Vy: P(y) ⇒¬W (y,x). 2. Ex: Vy: P(y) ^ W (y,x) ⇒ ¬³z : P(z) ^ G(z, x). 3. Vx: (vy: P(y) ^ W (y,x) ⇒ ¬³z : P(z) ^ G(z, x)). 4. 3x : P(x) ^ \y: (W(x,y) ⇒¬G(x, y)). 5. Ex: P(x) ^ (Vy: W(x, y) ⇒\z¬G(x, z)). 6. Ex: Vy: P(y) ^ W (y,x) ⇒ ¬³z: P(z) ^ G(z, x). 7. Ex: Vy: P(y) ^ ¬W(y, x).

1. Let G(x, y) denote that x gets y; W(x, y) denote that x wants y, and P(x) denote that x is a person. Match the following sentences with their equivalent sentence of predicate logic: a. If everyone wants something, then no one gets it. b. Some people want only things they don't get. c. There is something that nobody wants. 1. Ex: Vy: P(y) ⇒¬W (y,x). 2. Ex: Vy: P(y) ^ W (y,x) ⇒ ¬³z : P(z) ^ G(z, x). 3. Vx: (vy: P(y) ^ W (y,x) ⇒ ¬³z : P(z) ^ G(z, x)). 4. 3x : P(x) ^ \y: (W(x,y) ⇒¬G(x, y)). 5. Ex: P(x) ^ (Vy: W(x, y) ⇒\z¬G(x, z)). 6. Ex: Vy: P(y) ^ W (y,x) ⇒ ¬³z: P(z) ^ G(z, x). 7. Ex: Vy: P(y) ^ ¬W(y, x).

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Description: (discrete structure) 1. Let G(x, y) denote that x gets y; W(x, y) denote that x wants y, and P(x) denote that x is aperson. Match the following sentences with their equivalent sentence of predicate logic:a. If everyone wants something, then no one ge

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

(discrete structure)

1. Let G(x, y) denote that x gets y; W(x, y) denote that x wants y, and P(x) denote that x is a
person. Match the following sentences with their equivalent sentence of predicate logic:
a. If everyone wants something, then no one gets it.
b. Some people want only things they don't get.
c. There is something that nobody wants.
1. 3x : Vy : P(y) → ¬W(y,x).
2. 3x : Vy : P(y) ^W (y, x) → ¬3z : P(z) A G(z, x).
3. Vr : (Vy : P(y) ^ W (y, x) → ¬3z : P(z) ^ G(z, x)).
4. 3r : P(x) A Vy : (w(x, y) →¬G(x, y)).
5. 3a : P(æ) ^ (Vy : W (2, y) = V2¬G(x, z)).
6. Ja : Vy : P(y) AW (y, x) → ¬3z : P(z) A G(z, x).
7. 3x : Vy : P(y) ^¬W(y, x).

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