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Section: Name: 1. Write the following statement as an English sentence: "Em EZ, VnE Z, m = n +5" 2. Write the following sentence using V, 3: "For all real numbers x, there exists a real number that satisfies > y. 3. Is the following a statement? Is it true or false? "If x > 0, then X x² + 1 > 0"

Section: Name: 1. Write the following statement as an English sentence: "Em EZ, VnE Z, m = n +5" 2. Write the following sentence using V, 3: "For all real numbers x, there exists a real number that satisfies > y. 3. Is the following a statement? Is it true or false? "If x > 0, then X x² + 1 > 0"

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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How can we write these questions as statements and vertify if true?
Section: Name: 1. Write the following statement as an English sentence: "Em EZ, VnE Z, m = n +5" 2. Write the following sentence using V, 3: "For all real numbers x, there exists a real number 3 that satisfies x > y. 3. Is the following a statement? Is it true or false? "If x > 0, then 5. Negate the following statements: (a) "If x is prime, then √ is not a rational number." (b) (Vx>0, 3y ER, y² = x) X x² + 1 4. Convert to symbolic logic: "For all real numbers x, either x is less than zero or x is greater or equal to zero." > 0" *The examples, section numbers are from Richard Hammach's "Book of Proof".
Transcribed Image Text:Section: Name: 1. Write the following statement as an English sentence: "Em EZ, VnE Z, m = n +5" 2. Write the following sentence using V, 3: "For all real numbers x, there exists a real number 3 that satisfies x > y. 3. Is the following a statement? Is it true or false? "If x > 0, then 5. Negate the following statements: (a) "If x is prime, then √ is not a rational number." (b) (Vx>0, 3y ER, y² = x) X x² + 1 4. Convert to symbolic logic: "For all real numbers x, either x is less than zero or x is greater or equal to zero." > 0" *The examples, section numbers are from Richard Hammach's "Book of Proof".
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Step 1

Note- As per the honor code, only 3 sub-parts can be answered at a time. Please post other sub-parts separately.

1

Given- The statement is: "∃m∈ℤ, ∀n∈ℤ, m=n+5"

To find- Write the given statement as an English sentence.

Explanation- 

The statement "∃m∈ℤ, ∀n∈ℤ, m=n+5" in English format is written by:

"There exist an integer m, for every integer n such that sum of n and 5 is equal to m." 

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