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1. Let N = x ≤ y². {1,2,3,4,...} be the familiar set of natural numbers. Let P(x, y) be the predicate that [General hint: since “P(x, y)" means exactly the same thing as "x

1. Let N = x ≤ y². {1,2,3,4,...} be the familiar set of natural numbers. Let P(x, y) be the predicate that [General hint: since “P(x, y)" means exactly the same thing as "x

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.2: Real Numbers
Problem 3E: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder...
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1. Let N = x ≤ y². {1,2,3,4,...} be the familiar set of natural numbers. Let P(x, y) be the predicate that [General hint: since “P(x, y)" means exactly the same thing as "x <y2" in this problem, go ahead and rewrite P(x, y) as x ≤ y² — or P(a, b) as a ≤ b², or P(A) as <A², or whatever any time you think it might make things easier for you to look at or think about.] [LaTeX: Make N with \mathbb{N}.] (a) Write the following statement in clear and graceful English; say whether the statement is true or false; and explain your true/false answer in a sentence or two. Statement: x ЄN, VyЄN, P(x, y). (i) Clear and graceful English: (ii) True or false: (iii) Explanation: (b) Write the following statement in clear and graceful English; say whether the statement is true or false; and explain your true/false answer in a sentence or two. Statement: y N, VEN, P(x, y). (i) Clear and graceful English: (ii) True or false: (iii) Explanation: (c) Write the following statement in clear and graceful English; say whether the statement is true or false; and explain your true/false answer in a sentence or two. Statement: VEN, yЄN, P(x, y). (i) Clear and graceful English: (ii) True or false: (iii) Explanation:
Transcribed Image Text:1. Let N = x ≤ y². {1,2,3,4,...} be the familiar set of natural numbers. Let P(x, y) be the predicate that [General hint: since “P(x, y)" means exactly the same thing as "x <y2" in this problem, go ahead and rewrite P(x, y) as x ≤ y² — or P(a, b) as a ≤ b², or P(A) as <A², or whatever any time you think it might make things easier for you to look at or think about.] [LaTeX: Make N with \mathbb{N}.] (a) Write the following statement in clear and graceful English; say whether the statement is true or false; and explain your true/false answer in a sentence or two. Statement: x ЄN, VyЄN, P(x, y). (i) Clear and graceful English: (ii) True or false: (iii) Explanation: (b) Write the following statement in clear and graceful English; say whether the statement is true or false; and explain your true/false answer in a sentence or two. Statement: y N, VEN, P(x, y). (i) Clear and graceful English: (ii) True or false: (iii) Explanation: (c) Write the following statement in clear and graceful English; say whether the statement is true or false; and explain your true/false answer in a sentence or two. Statement: VEN, yЄN, P(x, y). (i) Clear and graceful English: (ii) True or false: (iii) Explanation:
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