Let RC RX R with {(x, y) |x² =5 y²}. Characterize R in terms of whether it is reflexive, irreflexive, symmetric, anti-symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. This is not a formal proof, but briefly explain your reasoning. Let f: R+ → N with f(x) = [x²]; that is, f(x) returns the square of x rounded up. Characterize f in terms of whether it is injective, surjective and/or bijective. This is not a formal proof, but briefly explain your reasoning.

Let RC RX R with {(x, y) |x² =5 y²}. Characterize R in terms of whether it is reflexive, irreflexive, symmetric, anti-symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. This is not a formal proof, but briefly explain your reasoning. Let f: R+ → N with f(x) = [x²]; that is, f(x) returns the square of x rounded up. Characterize f in terms of whether it is injective, surjective and/or bijective. This is not a formal proof, but briefly explain your reasoning.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...

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