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Question 13. For each item below, describe a function f : X → Y satisfying the given require- ments. You can use pictures, write out the ordered pairs, give a formula, etc. to describe your functions. Assume the sets X and Y are finite sets (and of course, you can change what X and Y are for each item!). 1. f : X →Y is surjective, but not injective. 2. f : X →Y is one-to-one, but not onto. 3. f :X → Y is bijective. 4. f: X → Y is neither one-to-one nor onto.

Question 13. For each item below, describe a function f : X → Y satisfying the given require- ments. You can use pictures, write out the ordered pairs, give a formula, etc. to describe your functions. Assume the sets X and Y are finite sets (and of course, you can change what X and Y are for each item!). 1. f : X →Y is surjective, but not injective. 2. f : X →Y is one-to-one, but not onto. 3. f :X → Y is bijective. 4. f: X → Y is neither one-to-one nor onto.

Advanced Engineering Mathematics
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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Please help me with question 13 from the picture that I uploaded. I would really appreciate it! :)

Question 13. For each item below, describe a function f : X → Y satisfying the given require- ments. You can use pictures, write out the ordered pairs, give a formula, etc. to describe your functions. Assume the sets X and Y are finite sets (and of course, you can change what X and Y are for each item!). 1. f : X → Y is surjective, but not injective. 2. f : X →Y is one-to-one, but not onto. 3. f : X → Y is bijective. 4. f : X →Y is neither one-to-one nor onto.
Transcribed Image Text:Question 13. For each item below, describe a function f : X → Y satisfying the given require- ments. You can use pictures, write out the ordered pairs, give a formula, etc. to describe your functions. Assume the sets X and Y are finite sets (and of course, you can change what X and Y are for each item!). 1. f : X → Y is surjective, but not injective. 2. f : X →Y is one-to-one, but not onto. 3. f : X → Y is bijective. 4. f : X →Y is neither one-to-one nor onto.
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