Question: Let f:x->Y and g:Y->Z be two functions (mapping ) (i) If f and g are both injective, then show that the composition of gof is

Let f:x->Y and g:Y->Z be two functions (mapping ) (i) If f and g are both injective, then show that the composition of gof is also injective.

Step by Step Solution

★★★★★

3.44 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that the composition of functions gof is injective when both ... View full answer

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 Accounting Questions!

Q:

A Treasury bond reaches maturity in 9 months. Assume that the Treasury bond has a coupon of 3% and the current price of the bond is $99,500. a. Estimate the bonds yield to maturity (based on...

Q:

Describe, and estimate the costs of, procedures to (a) insert a new item into an existing heap; (b) delete the topmost item from a non-empty heap; (c) starting from an array holding N items in...

Q:

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

Q:

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

Q:

4 Let f n 3n 5 and g n n be two functions defined on Z Which of the functions f g fog gof are injective Please explain precisely why 5 Show that the operation r y x y xy is commutative associative...

Q:

Definition reminders: A function f from A to B, written f: A + B is a relation f C Ax B such that, if a fb and a fb, then b=W. We write f(a) for the unique b such that a fb. Composition of functions...

Q:

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

Problem 1 (0.5 points) Prove the following proposition: Let X,Y,Z be sets, and f:XYand g:YZ be functions. If gof is surjective, then g is surjective. Problem 2 (0.5 points) Prove the following...

Q:

Provide an appropriate query to show that the above program can give an incorrect result. [4 marks] (b) Explain the cause of the error. [6 marks] (c) Suggest a correction. [5 marks] (d) Write a...

Q:

MATH 109 FALL 2016 SAMPLE MIDTERM 2 Instructions: Justify all of your answers, and show your work. You may use the result of one part of a problem in the proof of a later part, even if you do not...

Q:

Using the HCF Balance Sheet on page 226-227 in Table 9A-1, how could you determine the amount of debt principal that will be retired during the next fiscal year? TABLE 9A-1 Harris Memorial Hospital...

Q:

12 - A power cycle operates between a reservoir at temperature T and a lower-temperature reservoir at 280 K. At steady state, the cycle develops 80 kW of power while rejecting 2000 kJ/min of energy...

Q:

TransactionTotal AssetsTotal LiabilitiesTotal Stockholder's EquityIssue common stock + + Issue preferred stock + + Purchase treasury stock + Sell treasury stock + + Declare cash dividend + Pay cash...

Q:

In 2012 Charlie Snyder opened Charlies Pets, a small retail shop selling pet supplies. On December 31, 2012, Charlies accounting records showed the following: Inventory on December 31, 2012 .... $...

Q:

A circular loop of wire is in a region of spatially uniform magnetic field, as shown in Fig. 29.31. The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or...

Q:

La-Z-Boy Inc. is one of the worlds largest manufacturers of furniture and is best known for its reclining chairs. The following data (in thousands) were adapted from the 2008 annual report of...

Q:

How did the new project selection process handle nonnumeric type projects? Risk? How did this new process alter new project proposals at HP?

Q:

Classify the following items as (a) Prepaid expense, (b) Unearned revenue, (c) Accrued revenue, or (d) Accrued expense. 1. A two-year premium paid on a fire insurance policy. 2. Fees earned but not...

Q:

Scenario You are a manager at ABC Corporation, and you manage a team of 20 employees. You conduct a weekly team meeting, which allows you to stress the expectations of each employee. You have...

Q:

An article in Computers & Electrical Engineering [Parallel Simulation of Cellular Neural Networks (1996, Vol. 22, pp. 6184)] considered the speedup of cellular neural networks (CNN) for a parallel...

Q:

Consider the visits that result in leave without being seen (LWBS) at an emergency department in Example 2-8. Assume that four visits that result in LWBS are to be randomly selected (without...

Q:

A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to schedule three knee, four hip, and five shoulder surgeries....

Q:

Two companies that manufacture batteries for electronics products have submitted their products to an independent testing agency. The agency tested 200 of each companys batteries and recorded the...

Q:

Wilson Construction and Concrete Company is known as a very progressive company that is willing to try new ideas to improve its products and service. One of the key factors of importance in concrete...

Q:

The Cell Tone Company sells cellular phones and airtime in several northwestern states. At a recent meeting, the marketing manager stated that the average age of its customers is under 40. This came...