Math 405 - Problem set 3 Find a functionf: Q → Q that is injective but not surjective. 1. Find a funotion
Math 405 - Problem set 3 Find a functionf: Q → Q that is injective but not surjective. 1. Find a funotion
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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![Math 405 - Problem set 3
1. Find a function f: Q → Q that is injective but not surjective.
Find a functionf: Q Q that is surjective but not injective.
Find a function f: Q → Q that is neither surjective nor injective.
Find a function f : Q → Q that is both surjective and injective but not the identity
function.
2.
4.
Find sets A and B, subsets C, and C2 of A, and a function f: A → B so that
(CiN C2) = (C1)N(C2).
Find sets A and B, subsets C and C2 of A, and a function f : A
ACIN C2) c f(Ci)NAC2).
7. Show that the sets [0, 1] and (0,1) are equinumerous.
8. Prove: Every infinte set has a denumerable subset.
9. Show that the set of polynomials with integer coefficients is countable.
- 5.
6.
B so that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe62057a3-ffe7-4ee8-bf67-81589e3d1b64%2Fa8c60a32-a1c8-4af4-94eb-a8a3eed7763a%2Flb21pb_processed.png&w=3840&q=75)
Transcribed Image Text:Math 405 - Problem set 3
1. Find a function f: Q → Q that is injective but not surjective.
Find a functionf: Q Q that is surjective but not injective.
Find a function f: Q → Q that is neither surjective nor injective.
Find a function f : Q → Q that is both surjective and injective but not the identity
function.
2.
4.
Find sets A and B, subsets C, and C2 of A, and a function f: A → B so that
(CiN C2) = (C1)N(C2).
Find sets A and B, subsets C and C2 of A, and a function f : A
ACIN C2) c f(Ci)NAC2).
7. Show that the sets [0, 1] and (0,1) are equinumerous.
8. Prove: Every infinte set has a denumerable subset.
9. Show that the set of polynomials with integer coefficients is countable.
- 5.
6.
B so that
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