Question: Let X be an arbitrary set and Y = {a} be a set with a single element. Show that when there is a unique function

Let X be an arbitrary set and Y = {a} be a set with a single element. Show that when there is a unique function f : X > Y, for each three cases: 1)injective, 2)surjective, 3)bijecti0n. Please describe left inverses of f, along with all the possible right inverses

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

here question: 2. (a) Show that the set 1C2 is a complex vector space with respect to the vector addition and scalar multiplication defined by II + Ell __ I1+y1+1 a $1 ._ 031+1 Is 29': ._ Ia+ya+1 3'...

in here P(A) is power set of(A) 1.Prove that A B iff P (A) P (B). 2. Prove that for any set A, A = P (A). 3. Suppose {Ai | i I} and {Bi | i I} are indexed families of sets. (a) Prove that iI (Ai...

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

Exercise 1.4.13 (SchroderBernstein Theorem). Assume there exists a 1 1 function f : X Y and another 11 function g : Y X. Follow the steps to show that there exists a 11, onto function h : X Y and...

f x x Let x be any arbitrary element of R then Right hand limit at x x lim f x lim f x h X X Institute of Lifelong Learning University of Delhi lim x h 40 lim x h 2xh 0 0 lim f x x X X Left hand...

ANSWER ALL QUESTIONS. BE SURE TO ANSWER 7.1.8. A balanced die is rolled 3 times. Let x1 be the number of times 1 appears and x2 be the number of times 2 appears. Work out the joint probability...

Plz help.... Consider the following economy. There is continuum of workers with mass 1, each endowed with L units of labor, and a continuum of goods of mass N. They have the same utility given by U =...

P6 (15 points). Analyze Quicksort: Recall the Quicksort algorithm. Sup- pose we are given a set of n distinct numbers, Ag = {x1, ..., Xn}. The goal is to sort them in the increasing order. In the...

Prove that the two properties of the hierarchy function ( see Section 5 . 2 . 3 ) allow only trees and single nodes as organizations of objects. Section 5 . 2 . 3 is as following: Let S be the set of...

This book contains examples for each step in the design process for several hy- pothetical business applications. One of these is Moon Launch Enterprise, which markets moon junkets to the business or...

An advertisment propose different prices to different users using data collected from cookies, that the users consented for data profiling. Which are the rights of the users considering Art 22 of...

In an agency relationship, which of the following is Rylie considered to be a produce agent independent contractor, partially disclose principal, personal assistant, disclose, principal, employer,...

i need help spving this problem please!! Problem 5-5 Presented below is the balance sheet of Sargent Corporation for the current year, 2017 LOSSOM CORPORATION BALANCE SHEET DECEMBER 31 2017 488,300...