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Please arrange in a correct order steps of the given argument in logical form. "Everyone in New Jersey lives within 50 miles of the ocean. Someone in New Jersey has never seen the ocean. Therefore, someone who lives within 50 miles of the ocean has never seen the ocean." v (+) 3x(P(x) ^ Q(x)) Existential generalization of (%) v (%) P(c) ^ Q(c) Conjunction from ($), (&) v (&) There is x=c in the domain such that P(c) Universal instantiation (*) v (*) VxP(x) Hypothesis Let P(x) = "x lives within 50 miles of the ocean", and Q(x) = "x has never seen the ocean" with the domain of the variable consisting of all people who live in New Jersey. The argument in the logical form: "Everyone in New Jersey lives within 50 miles of the ocean"= VxP(x) v "Someone in New Jersey has never seen the ocean" = 3xQ(x) Someone who lives within 50 miles of the ocean has never seen the ocean = 3x(P(x)^ Q(x))

Please arrange in a correct order steps of the given argument in logical form. "Everyone in New Jersey lives within 50 miles of the ocean. Someone in New Jersey has never seen the ocean. Therefore, someone who lives within 50 miles of the ocean has never seen the ocean." v (+) 3x(P(x) ^ Q(x)) Existential generalization of (%) v (%) P(c) ^ Q(c) Conjunction from ($), (&) v (&) There is x=c in the domain such that P(c) Universal instantiation (*) v (*) VxP(x) Hypothesis Let P(x) = "x lives within 50 miles of the ocean", and Q(x) = "x has never seen the ocean" with the domain of the variable consisting of all people who live in New Jersey. The argument in the logical form: "Everyone in New Jersey lives within 50 miles of the ocean"= VxP(x) v "Someone in New Jersey has never seen the ocean" = 3xQ(x) Someone who lives within 50 miles of the ocean has never seen the ocean = 3x(P(x)^ Q(x))

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The argument in the logical form: 1. "Everyone in New Jersey lives within 50 miles of the ocean" is represented as ∀xP(x). 2. "Someone in New Jersey has never seen the ocean" is represented as ∃xQ(x). 3. "Someone who lives within 50 miles of the ocean has never seen the ocean" is represented as ∃x(P(x) ∧ Q(x)). Explanation: - The symbol ∀ represents "for all," indicating a universal statement about New Jersey residents. - The symbol ∃ represents "there exists," indicating the presence of at least one individual fulfilling the condition. - P(x) indicates that person x lives within 50 miles of the ocean. - Q(x) indicates that person x has never seen the ocean. - The conjunction ∧ shows a combination of two conditions being true simultaneously for an individual. Steps: - (#) ∃xQ(x): There exists a person in New Jersey who has never seen the ocean. - ($) There is an x=c in the domain for which Q(c): This is existential instantiation, which selects a specific individual, c, who fulfills Q(x). These logical translations help in analyzing arguments using formal logic.
Transcribed Image Text:The argument in the logical form: 1. "Everyone in New Jersey lives within 50 miles of the ocean" is represented as ∀xP(x). 2. "Someone in New Jersey has never seen the ocean" is represented as ∃xQ(x). 3. "Someone who lives within 50 miles of the ocean has never seen the ocean" is represented as ∃x(P(x) ∧ Q(x)). Explanation: - The symbol ∀ represents "for all," indicating a universal statement about New Jersey residents. - The symbol ∃ represents "there exists," indicating the presence of at least one individual fulfilling the condition. - P(x) indicates that person x lives within 50 miles of the ocean. - Q(x) indicates that person x has never seen the ocean. - The conjunction ∧ shows a combination of two conditions being true simultaneously for an individual. Steps: - (#) ∃xQ(x): There exists a person in New Jersey who has never seen the ocean. - ($) There is an x=c in the domain for which Q(c): This is existential instantiation, which selects a specific individual, c, who fulfills Q(x). These logical translations help in analyzing arguments using formal logic.
**Logical Argument Transcription:** **Title:** Arranging Argument Steps in Logical Form **Statement:** “Everyone in New Jersey lives within 50 miles of the ocean. Someone in New Jersey has never seen the ocean. Therefore, someone who lives within 50 miles of the ocean has never seen the ocean.” **Logical Steps in Correct Order:** 1. **Existential Generalization of (%)** ∃x(P(x) ∧ Q(x)) 2. **Conjunction from ($), (&)** P(c) ∧ Q(c) 3. **Universal Instantiation (*)** There is x=c in the domain such that ρ(c) 4. **Hypothesis** ∀xP(x) **Logical Explanation:** - **Let P(x):** "x lives within 50 miles of the ocean" - **Let Q(x):** "x has never seen the ocean" - The domain is all people who live in New Jersey. **Argument in Logical Form:** - "Everyone in New Jersey lives within 50 miles of the ocean." → ∀xP(x) - "Someone in New Jersey has never seen the ocean." → ∃x Q(x) - Therefore, "Someone who lives within 50 miles of the ocean has never seen the ocean." → ∃x(P(x) ∧ Q(x))
Transcribed Image Text:**Logical Argument Transcription:** **Title:** Arranging Argument Steps in Logical Form **Statement:** “Everyone in New Jersey lives within 50 miles of the ocean. Someone in New Jersey has never seen the ocean. Therefore, someone who lives within 50 miles of the ocean has never seen the ocean.” **Logical Steps in Correct Order:** 1. **Existential Generalization of (%)** ∃x(P(x) ∧ Q(x)) 2. **Conjunction from ($), (&)** P(c) ∧ Q(c) 3. **Universal Instantiation (*)** There is x=c in the domain such that ρ(c) 4. **Hypothesis** ∀xP(x) **Logical Explanation:** - **Let P(x):** "x lives within 50 miles of the ocean" - **Let Q(x):** "x has never seen the ocean" - The domain is all people who live in New Jersey. **Argument in Logical Form:** - "Everyone in New Jersey lives within 50 miles of the ocean." → ∀xP(x) - "Someone in New Jersey has never seen the ocean." → ∃x Q(x) - Therefore, "Someone who lives within 50 miles of the ocean has never seen the ocean." → ∃x(P(x) ∧ Q(x))
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