Question: Complete the following proofs. Letf:AB be a function with finite domain and range. Suppose that|Dom(f)|=n and|R an(f)|=m.Letf:AB be a function with finite domain and range.

Complete the following proofs. Letf:AB be a function with finite domain and range. Suppose that|Dom(f)|=n and|R an(f)|=m.Letf:AB be a function with finite domain and range. Suppose that|Dom(f)|=n and|R an(f)|=m. Prove that if f is one to one, then m=n and if f is not one to one, then m < n. Letf:ABandg:BC. Prove that if f and g are onto function, then gf is onto.

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 Databases Questions!

Q:

Complete the following proof Let f:ABbe a function with finite domain and range. Suppose that|Dom(f)|=nand|Ran(f)|=m. Letf:ABbe a function with finite domain and range. Suppose...

Q:

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

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:

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Q:

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Q:

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

Induction (#1-3, 24 pts) #1 . Prove by induction that8 + 15 + 22 + 29 + ... +(7 n + 1) = n (7 n + 9)/2for all n N . #2. Prove the summation formula for the following particular finite geometric...

Q:

The director wants to conduct the seminar 47 working days from now . What is the probability that everything will be ready in time? Time Estimates (days) Most Activity Optimistic Likely Pessimistic...

Q:

ADI apply the ADI method to the Dirichlet problem in Prob 5, using the grid in Fig. 455, as before and starting values zero.

Q:

Give an example. Choose the correct answer below. A. An investor has a starting principal Pequals$3000 and an accumulated value of Aequals$8400 after Yequals4 years. The annual return is zero. B. An...

Q:

EQ 0 7 Q 5 . Wat is de entropy feroaring fan it gas, ferwaarme yn in steady - flow proses by likern ch atmosfearyske druk, as ( a ) 8 0 0 kJ wurdt tafoege oan 1 0 mol fan ethyleen yn earste ynst nsje...

Q:

After Column and Data Types have been set in the Mining Structure, what is the next step?

Q:

What needs to occur after any Structural or Variable setting change in SSAS Mining Structures?

Q:

For the highest GS Pay Grade Group (1115) in the Federal Government, what are the chances of Females being included? Do Females have longer service statistics in that Group?