1. Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Let R be the relation on ♬ defined by: For all f, gЄ F, fRg go f(1) = 2. (a) Is R reflexive, symmetric, antisymmetric, transitive? Prove your answers. (b) Is it true that for all functions ƒ Є F, there exists a function 9 € Ƒ so that fRg? Prove your answer. (c) Is it true that for all functions g = F, there exists a function f = Ƒ so that fRg? Prove your answer. (d) How many functions f = F are there so that fRf? Please simplify your answer to a number and provide your recipe.

1. Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Let R be the relation on ♬ defined by: For all f, gЄ F, fRg go f(1) = 2. (a) Is R reflexive, symmetric, antisymmetric, transitive? Prove your answers. (b) Is it true that for all functions ƒ Є F, there exists a function 9 € Ƒ so that fRg? Prove your answer. (c) Is it true that for all functions g = F, there exists a function f = Ƒ so that fRg? Prove your answer. (d) How many functions f = F are there so that fRf? Please simplify your answer to a number and provide your recipe.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 63E

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