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Are the following statements? Which are true or false?

Are the following statements? Which are true or false?

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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Are the following statements? Which are true or false?
factoring or It is False that the number x andy are bot real quadratic formula (b) The numbers x and y are both odd. (c) The square of every real number is non-negative. It is false that the square of non-negative 15 Additional Problems 1. Convert to English, state if true or false: Vn € Z, 3X CN, X| = n. every 2. Convert to a statement with V and 3, state if true or false: There exists a real number y, such that for every real number x, the product xy = 1. YER, for V*ER Product xy = 1 It's False because X=Q Not existing 3. Is this a statement? Is it true or false? "If f is a rational function, then f has an asymptote." nu. 4. Convert to symbolic logic: "If x is a rational number and x 0, then tan(x) is not a rational number." Negate the following sentence, and write in logic: "There exists a natural number n, such that n² = n." for any given natural number n, it has ya In VN, n²n *The examples, section numbers are from Richard Hammack's "Book of Proof".
Transcribed Image Text:factoring or It is False that the number x andy are bot real quadratic formula (b) The numbers x and y are both odd. (c) The square of every real number is non-negative. It is false that the square of non-negative 15 Additional Problems 1. Convert to English, state if true or false: Vn € Z, 3X CN, X| = n. every 2. Convert to a statement with V and 3, state if true or false: There exists a real number y, such that for every real number x, the product xy = 1. YER, for V*ER Product xy = 1 It's False because X=Q Not existing 3. Is this a statement? Is it true or false? "If f is a rational function, then f has an asymptote." nu. 4. Convert to symbolic logic: "If x is a rational number and x 0, then tan(x) is not a rational number." Negate the following sentence, and write in logic: "There exists a natural number n, such that n² = n." for any given natural number n, it has ya In VN, n²n *The examples, section numbers are from Richard Hammack's "Book of Proof".
1. (a) Write the following statements as English sentences, and state whether they are true or false. for i. V ER, En EN, x ≥ 0. a natural number True ii. VnE Z, 3m € Z, m = n +5. For number m any 5 Worksheet real number x, there any n to make x 20 whole number n, there carst a whe to make n=ntt True (b) Write the following statements using quantifiers and 3. i. For all x € R, if x is greater than 2, then ² is greater than 4. (b) If p is a prime number, then p is odd. ii. For all x ER there exists y E R such that f(y) > f(x). (Can you think of a function f which has this property?) 2. Are the following statements? Which are true, which are false? (a) If x = R, then x² +1> 0. stakement (c) If a function f is differentiable on R, then f is continuous on R. Sement Convert the following statements to symbolic logic: (a) For every prime number p there is another prime number q such that q> p. (Prime (P)) = 9 (Prime (9) N(P<q)] Prime G = 9 15 € 1: and V means every there is 3 means -) If sin x < 0, then it is not the case that 0≤x≤T.
Transcribed Image Text:1. (a) Write the following statements as English sentences, and state whether they are true or false. for i. V ER, En EN, x ≥ 0. a natural number True ii. VnE Z, 3m € Z, m = n +5. For number m any 5 Worksheet real number x, there any n to make x 20 whole number n, there carst a whe to make n=ntt True (b) Write the following statements using quantifiers and 3. i. For all x € R, if x is greater than 2, then ² is greater than 4. (b) If p is a prime number, then p is odd. ii. For all x ER there exists y E R such that f(y) > f(x). (Can you think of a function f which has this property?) 2. Are the following statements? Which are true, which are false? (a) If x = R, then x² +1> 0. stakement (c) If a function f is differentiable on R, then f is continuous on R. Sement Convert the following statements to symbolic logic: (a) For every prime number p there is another prime number q such that q> p. (Prime (P)) = 9 (Prime (9) N(P<q)] Prime G = 9 15 € 1: and V means every there is 3 means -) If sin x < 0, then it is not the case that 0≤x≤T.
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