15. Determine whether the function f: Z x Z Z is onto if a) f(m, n) =m+n. b) f(m, n) = m² + n². c) f(m,n) — т. d) f(m, n) = |n|. e) f (m,п) — т -п. %3D
15. Determine whether the function f: Z x Z Z is onto if a) f(m, n) =m+n. b) f(m, n) = m² + n². c) f(m,n) — т. d) f(m, n) = |n|. e) f (m,п) — т -п. %3D
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
15
![a) f(a)= b, f(b) = a, ƒ(c) = c, f(d) = d
b) f(a) = b, f(b) = b, ƒ(c) = d, f (d) = c
c) f(a)= d, f(b) = b, f(c) = c, f (d) = d
11. Which functions in Exercise 10 are onto?
%3D
%3D
12. Determine whether each of these functions from Z
is one-to-one.
a) f(n)=n – 1
c) f(n)=n³
13. Which functions in Exercise 12 are onto?
14. Determine whether f:Z x Z Z is onto if
a) f(m,n) = 2m-n.
b) f(m,n) = m² – n².
c) f(m, n)= m+n+ 1.
d) f(m,n) Im| - |n|.
e) f(m,n) - т?-4.
15. Determine whether the function f: Z x Z Z is onto
b) f(n)=n² +1
d) f(n)= [n/2]
if
a) f(m,n) — т+п.
b) f(m, n) = m² + n².
c) f(m, n) =
d) f(m, n) = |n|.
e) f(m, n) =
16. Consider these functions from the set of students in a
discrete mathematics class. Under what conditions is the
function one-to-one if it assigns to a student his or her
= m.
m-n.
a) mobile phone number.
b) student identification number.
c) final grade in the class.
d) home town.
17. Consider these funotion](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0871111-955c-42b8-b934-16ba62370e3b%2F2b95ed10-00ad-4ab2-bd91-b2049ac1e1d0%2Fq3arn1g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) f(a)= b, f(b) = a, ƒ(c) = c, f(d) = d
b) f(a) = b, f(b) = b, ƒ(c) = d, f (d) = c
c) f(a)= d, f(b) = b, f(c) = c, f (d) = d
11. Which functions in Exercise 10 are onto?
%3D
%3D
12. Determine whether each of these functions from Z
is one-to-one.
a) f(n)=n – 1
c) f(n)=n³
13. Which functions in Exercise 12 are onto?
14. Determine whether f:Z x Z Z is onto if
a) f(m,n) = 2m-n.
b) f(m,n) = m² – n².
c) f(m, n)= m+n+ 1.
d) f(m,n) Im| - |n|.
e) f(m,n) - т?-4.
15. Determine whether the function f: Z x Z Z is onto
b) f(n)=n² +1
d) f(n)= [n/2]
if
a) f(m,n) — т+п.
b) f(m, n) = m² + n².
c) f(m, n) =
d) f(m, n) = |n|.
e) f(m, n) =
16. Consider these functions from the set of students in a
discrete mathematics class. Under what conditions is the
function one-to-one if it assigns to a student his or her
= m.
m-n.
a) mobile phone number.
b) student identification number.
c) final grade in the class.
d) home town.
17. Consider these funotion
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