• Write the negation of the statement in symbolic form in which the nega- tion symbol is not used. • rite a useful negation of the statement in an English sentence that does not use the symbols for quantifiers. (a) (3x € Q) (x > v2). (b) (Vx e Q) (x² – 2+ 0). (c) (Vx e Z) (x is even or x is odd). (d) (3x e Q) ( v2 < x < v3). Note: The sentence “/7 < x < v3" is actually a conjuction. It means /2 < x and x < /3. * (e) (Vx e Z) (If x² is odd, then x is odd). (f) (¥n e N) [If n is a perfect square, then (2" – 1) is not a prime num- ber]. (9) (Vn e N) (n2 – n + 41 is a prime number)
• Write the negation of the statement in symbolic form in which the nega- tion symbol is not used. • rite a useful negation of the statement in an English sentence that does not use the symbols for quantifiers. (a) (3x € Q) (x > v2). (b) (Vx e Q) (x² – 2+ 0). (c) (Vx e Z) (x is even or x is odd). (d) (3x e Q) ( v2 < x < v3). Note: The sentence “/7 < x < v3" is actually a conjuction. It means /2 < x and x < /3. * (e) (Vx e Z) (If x² is odd, then x is odd). (f) (¥n e N) [If n is a perfect square, then (2" – 1) is not a prime num- ber]. (9) (Vn e N) (n2 – n + 41 is a prime number)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
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3 B and D
![3. For each of the following statements
• Write the statement as an English sentence that does not use the sym-
bols for quantifiers.
A NG SA
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 > v2).
(b) (Vx e Q) (x² – 2 + 0).
* (c) (Vx e Z) (x is even or x is odd).
(d) (3x € Q) ( v2 < x < v3). Note: The sentence “/2 < x < 3" is
actually a conjuction. It means /2 < x and x < /3.
* (e) (Vx e Z) (If x² is odd, then x is odd).
(f) (Vn e N) [If n is a perfect square, then (2" – 1) is not a prime num-
ber].
(g) (Vn e N) (n² – n + 41 is a prime number).
* (h) (3x e R) (cos(2x) = 2(cos x)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68628b5-f384-4ba7-a04f-a8f64dbf4c73%2F67d824d5-b3b9-4131-a33b-b0fa7c660007%2F2weam52t_processed.png&w=3840&q=75)
Transcribed Image Text:3. For each of the following statements
• Write the statement as an English sentence that does not use the sym-
bols for quantifiers.
A NG SA
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 > v2).
(b) (Vx e Q) (x² – 2 + 0).
* (c) (Vx e Z) (x is even or x is odd).
(d) (3x € Q) ( v2 < x < v3). Note: The sentence “/2 < x < 3" is
actually a conjuction. It means /2 < x and x < /3.
* (e) (Vx e Z) (If x² is odd, then x is odd).
(f) (Vn e N) [If n is a perfect square, then (2" – 1) is not a prime num-
ber].
(g) (Vn e N) (n² – n + 41 is a prime number).
* (h) (3x e R) (cos(2x) = 2(cos x)).
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