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).
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text: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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