3. For each of the following statements BY NG SA Write the statement as an English sentence that does not use the sym- bols for quantifiers. 2.4. Quantifiers and Negations 75 • Write the negation of the statement in symbolic form in which the nega- tion symbol is not used. • Write a useful negation of the statement in an English sentence that does not use the symbols for quantifiers. *(a) (3x € Q) (x > √2). (b) (VxQ) (x² - 2 = 0). * (c) (Vx Z) (x is even or x is odd). (d) (3x € Q) ( √² < x < √√3). Note: The sentence “√2 < x < √3” is actually a conjuction. It means √2
3. For each of the following statements BY NG SA Write the statement as an English sentence that does not use the sym- bols for quantifiers. 2.4. Quantifiers and Negations 75 • Write the negation of the statement in symbolic form in which the nega- tion symbol is not used. • Write a useful negation of the statement in an English sentence that does not use the symbols for quantifiers. *(a) (3x € Q) (x > √2). (b) (VxQ) (x² - 2 = 0). * (c) (Vx Z) (x is even or x is odd). (d) (3x € Q) ( √² < x < √√3). Note: The sentence “√2 < x < √3” is actually a conjuction. It means √2
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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![3. For each of the following statements
BY NG SA
Write the statement as an English sentence that does not use the sym-
bols for quantifiers.
2.4. Quantifiers and Negations
75
• Write the negation of the statement in symbolic form in which the nega-
tion symbol is not used.
• Write a useful negation of the statement in an English sentence that
does not use the symbols for quantifiers.
*(a) (3x € Q) (x > √2).
(b) (VxQ) (x² - 2 = 0).
* (c) (Vx € Z) (x is even or x is odd).
(d) (3x € Q) ( √² < x < √√3). Note: The sentence “√2 < x < √3” is
actually a conjuction. It means √2<x and x < √√3.
* (e) (vx € Z) (If x² is odd, then x is odd).
(f) (\n N) [If n is a perfect square, then (2" – 1) is not a prime num-
ber].
(g) (VnN) (n² - n +41 is a prime number).
(h) (3x € R) (cos(2x) = 2(cosx)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff800a840-0309-4834-92a3-4244363b7afa%2F1f685cd0-4a99-413d-8a5a-72658d83b397%2Fvh1whde_processed.png&w=3840&q=75)
Transcribed Image Text:3. For each of the following statements
BY NG SA
Write the statement as an English sentence that does not use the sym-
bols for quantifiers.
2.4. Quantifiers and Negations
75
• Write the negation of the statement in symbolic form in which the nega-
tion symbol is not used.
• Write a useful negation of the statement in an English sentence that
does not use the symbols for quantifiers.
*(a) (3x € Q) (x > √2).
(b) (VxQ) (x² - 2 = 0).
* (c) (Vx € Z) (x is even or x is odd).
(d) (3x € Q) ( √² < x < √√3). Note: The sentence “√2 < x < √3” is
actually a conjuction. It means √2<x and x < √√3.
* (e) (vx € Z) (If x² is odd, then x is odd).
(f) (\n N) [If n is a perfect square, then (2" – 1) is not a prime num-
ber].
(g) (VnN) (n² - n +41 is a prime number).
(h) (3x € R) (cos(2x) = 2(cosx)).
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