Deal with it Question 1relation R on F as follows: for all f, g € F, fRg if and only if there exists x E A so that f(x) < g(x).Let A = {1,2, 3, 4}. Let F be the set of all functions from A to A. Define a(a) Is R reflexive? Prove your answer.(b) Is R antisymmetric? Prove your answer.(c) Is R transitive? Prove your answer.(d) Is it true that for all f E F, there exists g E F so that f Rg? Prove your answer.

It is given that A=1, 2, 3, 4 and ℱ is the collection of functions from A to A. The relation R on…

Answered: Question 1 Let A = {1,2, 3, 4}. Let F…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 62E

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Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Define arelation R on F as follows: for all f,g ∈ F, fRg if and only if there exists x ∈ A so that f(x) ≤ g(x). Is R antisymmetric? Prove your answer.
true or False? Prove your answer! a) Suppose h:R→R is not one-to-one, and suppose a, b∈R with a≠b. Then h(a) =h(b). b) Suppose g:R→R is a function such that for every x∈R, there exists y∈R such that g(x)≠y . Then g is not onto.
Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Define arelation R on F as follows: for all f,g ∈ F, fRg if and only if there exists x ∈ A so that f(x) ≤ g(x). (a) Is R reflexive? Prove your answer.(b) Is R antisymmetric? Prove your answer.(c) Is R transitive? Prove your answer.(d) Is it true that for all f ∈ F, there exists g ∈ F so that fRg? Prove your answer.
true or false? PROVE YOUR ANSWER b) If f :N→N and g :N→N are functions such that f is not onto but fg is onto, then g is onto. The claim is of answer: prove of answer

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Question 1 Let A = {1,2, 3, 4}. Let F be the set of all functions from A to A. Define a relation R on F as follows: for all f,g e F, fRg if and only if there exists r E A so that f(x) < g(x). (a) Is R reflexive? Prove your answer.