Characterize the relations in questions 14 and 15 in terms of whether each is reflexive, irreflexive, symmetric, anti- symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. These are not proofs but you must justify your answers. 14. (15) R S R × R with {(x, y)|x3 = -y³} 15. (15) R C R+ × R+ with R = {(x,y)||x| = ]y]}, that is, x and y are equal when both are rounded down. Characterize the functions in questions 16 and 17 in terms of whether each are injective, surjective and/or bijective. These are not proofs but you must justify your answers. 16. (10) f: N+ → N* and let f(x) return the sum of the digits of x. 17. (10) f:R+ →N+ with f(x)=x²]; that is, f(x)-returns the square of x-rounded up.
Characterize the relations in questions 14 and 15 in terms of whether each is reflexive, irreflexive, symmetric, anti- symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. These are not proofs but you must justify your answers. 14. (15) R S R × R with {(x, y)|x3 = -y³} 15. (15) R C R+ × R+ with R = {(x,y)||x| = ]y]}, that is, x and y are equal when both are rounded down. Characterize the functions in questions 16 and 17 in terms of whether each are injective, surjective and/or bijective. These are not proofs but you must justify your answers. 16. (10) f: N+ → N* and let f(x) return the sum of the digits of x. 17. (10) f:R+ →N+ with f(x)=x²]; that is, f(x)-returns the square of x-rounded up.
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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![Characterize the relations in questions 14 and 15 in terms of whether each is reflexive, irreflexive, symmetric, anti-
symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. These are not proofs but
you must justify your answers.
14. (15) R CR × R with {(x, y)|x³ = -y³}
15. (15) R C R+ × R+ with R
{(x, y)||x] = Ly]}, that is, x and y are equal when both are rounded down.
Characterize the functions in questions 16 and 17 in terms of whether each are injective, surjective and/or bijective.
These are not proofs but you must justify your answers.
(10) f: N* → N† and let f (x) return the sum of the digits of x.
17. (10) f: R+ → N+with f(x)= fx²]; that is, f(x) returns the square of x-rounded up.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99889170-b357-4807-8a0a-b4a05be508b5%2F8c0dd16a-bc18-40c4-8f04-99ef1f9ad935%2Fgyguicb_processed.png&w=3840&q=75)
Transcribed Image Text:Characterize the relations in questions 14 and 15 in terms of whether each is reflexive, irreflexive, symmetric, anti-
symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. These are not proofs but
you must justify your answers.
14. (15) R CR × R with {(x, y)|x³ = -y³}
15. (15) R C R+ × R+ with R
{(x, y)||x] = Ly]}, that is, x and y are equal when both are rounded down.
Characterize the functions in questions 16 and 17 in terms of whether each are injective, surjective and/or bijective.
These are not proofs but you must justify your answers.
(10) f: N* → N† and let f (x) return the sum of the digits of x.
17. (10) f: R+ → N+with f(x)= fx²]; that is, f(x) returns the square of x-rounded up.
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