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) ⇒ ¬‡z : P(z) ^ G(z, x)). 4. Ex : P(x) ^ Vy: (W(x, y) ⇒¬G(x, y)). 5. 3x : 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) ⇒ ¬‡z : P(z) ^ G(z, x)). 4. Ex : P(x) ^ Vy: (W(x, y) ⇒¬G(x, y)). 5. 3x : 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).

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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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) ^ G(z, x).
3. Væ : (Vy : P(y) ^W (y, x) → ¬3z : P(2) ^ G(z, x)).
4. Ja : P(x) ^ Vy : (W(x,y) → ¬G(x, y)).
5. Jr : P(x) ^ (Vy : W (x, y) → V2¬G(x, z)).
6. 3x : Vy : P(y) ^W (y, x) = ¬3z : P(z) ^ G(z, x).
7. Jx : Vy : P(y) ^ ¬W(y, x).

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