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 butyou 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.

Answered: Image /qna-images/answer/8c0dd16a-bc18-40c4-8f04-99ef1f9ad935.jpg

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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.
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Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.