19. Suppose f :X Y is a function. Which of the following are possible? Explain. a. fis injective but not surjective. b. fis surjective but not injective. С. |X| = |Y| and f is injective but not surjective. d. X| = |Y| and f is surjective but not injective. e. X| = |Y|, X and Y are finite, and f is injective but not surjective. f. X = |Y|, X and Y are finite, and f is surjecive but not injective.
19. Suppose f :X Y is a function. Which of the following are possible? Explain. a. fis injective but not surjective. b. fis surjective but not injective. С. |X| = |Y| and f is injective but not surjective. d. X| = |Y| and f is surjective but not injective. e. X| = |Y|, X and Y are finite, and f is injective but not surjective. f. X = |Y|, X and Y are finite, and f is surjecive but not injective.
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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Question
Question 19.
Please explain why for me.
![b. there is a surjective function f : XY? Explain.
there is a bijective function f : X Y? Explain.
С.
19. Suppose f : X Y is a function. Which of the following are possible?
Explain.
f is injective but not surjective.
а.
b. fis surjective but not injective.
C. X| = |Y| and f is injective but not surjective.
d. X| = |Y| and f is surjective but not injective.
e. X = |Y], X and Y are finite, and f is injective but not surjective.
f. X| = |Y|, X and Y are finite, and f is surjecive but not injective.
20. Let f : X →Y and g : Y→ Z be functions. We can define the composition
of f and g to be the function gof: X→ Z for which the image of each a E X is
9(f(¤)). That is, plug a into f, then plug the result into g (just like composition in
algebra and calculus).
a.
If f and g are both injective, must gof be injective? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febe9eacc-a056-497e-88ba-73962c29657e%2F69946008-d910-417c-bbc4-5a0fe08c47bd%2F0x6y3i7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b. there is a surjective function f : XY? Explain.
there is a bijective function f : X Y? Explain.
С.
19. Suppose f : X Y is a function. Which of the following are possible?
Explain.
f is injective but not surjective.
а.
b. fis surjective but not injective.
C. X| = |Y| and f is injective but not surjective.
d. X| = |Y| and f is surjective but not injective.
e. X = |Y], X and Y are finite, and f is injective but not surjective.
f. X| = |Y|, X and Y are finite, and f is surjecive but not injective.
20. Let f : X →Y and g : Y→ Z be functions. We can define the composition
of f and g to be the function gof: X→ Z for which the image of each a E X is
9(f(¤)). That is, plug a into f, then plug the result into g (just like composition in
algebra and calculus).
a.
If f and g are both injective, must gof be injective? Explain.
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