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Suppose f : X → Y is a function. Which of the following are possible? Explain. (a) f is injective but not surjective. (b) f is 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. %3D (f) |X| = |Y|, X and Y are finite, and f is surjective but not injective.

Suppose f : X → Y is a function. Which of the following are possible? Explain. (a) f is injective but not surjective. (b) f is 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. %3D (f) |X| = |Y|, X and Y are finite, and f is surjective but not injective.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Suppose f : X → Y is a function. Which of the following are possible? Explain. (a) f is injective but not surjective. (b) f is 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. %3D (f) |X| = |Y|, X and Y are finite, and f is surjective but not injective.
Transcribed Image Text:Suppose f : X → Y is a function. Which of the following are possible? Explain. (a) f is injective but not surjective. (b) f is 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. %3D (f) |X| = |Y|, X and Y are finite, and f is surjective but not injective.
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