Are the following statements? Which are true or false?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Are the following statements? Which are true or false?
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e21668-df36-4535-9b97-aa4a56ba16f0%2F8a9538ce-3276-49ae-8596-321783e527f9%2F6x2fw4o_processed.jpeg&w=3840&q=75)
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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