19. Suppose f : X →Y is a function. Which of the following are possible? Explain. a. f is injective but not surjective. 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. е. |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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Can you explain or give a detail example of (e) and (f) for me. I actually tried to understand it but it is still difficult for me...Give me a good example!
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.
|X| = |Y| and f is injective but not surjective.
С.
d. X = |Y| and f is surjective but not injective.
%3D
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.
Transcribed Image Text: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. |X| = |Y| and f is injective but not surjective. С. d. X = |Y| and f is surjective but not injective. %3D 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.
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