Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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