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Let A be the first-order logic formula \x³y²(x, ƒ(v), a), where P is a relation symbol, ƒ is a function symbol, and a is an individual symbol. Let D be the set {1, 2, 3}. (a) Give a valuation, v₁, over the domain D, such that A¹ = 1. Explain why your choice of v₁ is correct. (b) Give a valuation, vo, over the domain D, such that A% = 0. Explain why your choice of Vo is correct.

Let A be the first-order logic formula \x³y²(x, ƒ(v), a), where P is a relation symbol, ƒ is a function symbol, and a is an individual symbol. Let D be the set {1, 2, 3}. (a) Give a valuation, v₁, over the domain D, such that A¹ = 1. Explain why your choice of v₁ is correct. (b) Give a valuation, vo, over the domain D, such that A% = 0. Explain why your choice of Vo is correct.

Advanced Engineering Mathematics
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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Let A be the first-order logic formula \x³y²(x, f(y), a), where P is a relation symbol, ƒ is a function symbol, and a is an individual symbol. Let D be the set {1, 2, 3}. (a) Give a valuation, v₁, over the domain D, such that A¹¹ = 1. Explain why your choice of v₁ is correct. (b) Give a valuation, vo, over the domain D, such that Ao = 0. Explain why your choice of Vo is correct.
Transcribed Image Text:Let A be the first-order logic formula \x³y²(x, f(y), a), where P is a relation symbol, ƒ is a function symbol, and a is an individual symbol. Let D be the set {1, 2, 3}. (a) Give a valuation, v₁, over the domain D, such that A¹¹ = 1. Explain why your choice of v₁ is correct. (b) Give a valuation, vo, over the domain D, such that Ao = 0. Explain why your choice of Vo is correct.
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