Math+150++F09-+Hwk+4+Solutions

Math+150++F09-+Hwk+4+Solutions - SOLUTIONS TO HOMEWORK 4...

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Unformatted text preview: SOLUTIONS TO HOMEWORK 4 MATH 150, FALL 09 Problem 1. Section 2.1/ Exercise 1 Part (a): ∀ x ( Nx → < x ) Part (b): ∀ x ( Nx → ( Ix → I 0)) Part (c): ∀ x ( Nx → ¬ ( x < 0)) Part (d): ∀ x ( Nx → ( ¬ Ix → ( ∀ y ( Ny → ( y < x → Iy )) → Ix ))) Part (e): ∀ x ( Nx → ¬∀ y ( Ny → y < x )) Part (f): ∀ x ( Nx → ¬∀ y ( Ny → ¬ ( y < x ))) Problem 2. Section 2.1/ Exercise 3 ¬∀ x ( a ∈ x ) ∧ ¬∀ x ( b ∈ x ) Problem 3. Section 2.1/ Exercise 5 Part (a): There are two possible interpretations and respective transla- tions: (1) “There is a person, which can be fooled at all times” ∃ x ( Px ∧ ∀ y ( Ty → Fxy )) iff ¬∀ x ( ¬ ( Px ∧ ∀ y ( Ty → Fxy )) iff ¬∀ x ( Px → ¬∀ y ( Ty → Fxy )) (2) “At all times you can find someone to fool” ∀ y ( Ty → ∃ x ( Px ∧ Fxy )) iff ∀ y ( Ty → ¬∀ x ( Px → ¬ Fxy )) Part (b): There are two possible interpretations and respective transla- tions: (1) “Every person can be fooled some time”...
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This note was uploaded on 11/16/2009 for the course MATH 120 taught by Professor Smith during the Spring '09 term at UC Irvine.

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Math+150++F09-+Hwk+4+Solutions - SOLUTIONS TO HOMEWORK 4...

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