Please write up proofs for the following problems.I need to answer them very clearly with step by step explant please ...Needed clear proof...Will be highly appreciated..Thank You 2. Let f: A –→ B and g: B → C be functions and suppose that gof: A → C is surjective. Prove thatg must be surjective and give an example to show that f need not be.

Here we use the property of composition of function.

Answered: Please write up proofs for the…

Please write up proofs for the following problems. I need to answer them very clearly with step by step explant please ...Needed clear proof...Will be highly appreciated..Thank You

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.3: Properties Of Composite Mappings (optional)

Problem 12E: Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.

See similar textbooks

Related questions

Q: n 1 (p > 0). NP+1 k=1

A: In this question, we need to find the integrable function from the given limit.

Q: What is the converse of the following sentence? If you drive over 65 miles per hour then you will…

A: Statement If you drive over 65 miles per hour then you will get a speeding ticket.

Q: Only a, c, e, g (non-starred problems). Thank you!

A: Note:Our guidelines we are supposed to answer only first three subpart . Kindly repost other subpart…

Q: need some assistance with problem #16, please?

A: Topic:- application of calculus

Q: For this problem, assume that all the odd numbers are equally likely, all the even numbers are…

A: It is given that P(3) = 5/18.

Q: 5. n=3

Q: The popular comic strip FoxTrot follows the off-the-wall lives of the Fox family. Youngest son Jason…

A: The problem A to Z is given by:

Q: Question 1: Suppose that 200 applicants for mountain climbing trip, the following facts are known:…

A: Question 1. Let A,B,C represents the groups of applicants with altitude sickness, breathing issue…

Q: f(1)= 9, meaning when a 1 is rolled on the die, the player is awarded 9 points. This interpretation…

A: In question we need to find domain.

Q: Activity II. Answer the following questions briefly and concisely. 1. If you are one of the clerks…

Q: Need assistance with problem #13 of the attachment. Thank you in advance.

A: We have given a series;

Q: Are my answer for this problem correct?

A: Introduction: Analysis of Big- O notation for the polynomial function is given by, If…

Q: For each of the following problems, imagine that you are on a strange and unusual island, the…

A: Knights are truth tellers Knaves are liars Given statements : C: All of us are knaves. D: Exactly…

Q: Need help with problem #7 of attachment. Thanks in advance

A: Consider the provided question, According to the given equation the graph of required region rotated…

Q: ould I please get some h

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Are those answers right?

A: The equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using…

Q: What would be the answer to these questions

A: We are given with the cylinder whose height is 15 ft and radius is 6 ft and need tot find the volume…

Q: For each of the following problems, imagine that you are on a strange and unusual island, the…

A: G-Exactly one of us is knave. ~G is more than one of us is knave. K-Knight KN-Knave…

Q: Answer and work shown for attached problem #3. Thank you in advance

A: Over the interval {a, b]

Q: For problem 10, 11, and 12 below: (i) State the requirement (ii) State the null and alternative…

Q: How to slove these problems

Q: Am I doing this problem wrong? These are the values I got, and

A: Given:y=-8cos5πx

Q: For the above question, why are they negative?

A: Using All-sin-tan-cos rule we know that: So in third quadrant, only tan and cot are positive. sin,…

Q: For problem 10, 11, and 12 below: (i) State the requirement (ii) State the null and alternative…

Q: For each of the following problems, imagine that you are on a strange and unusual island, the…

A: We are given that Knights always tell truth Knaves only lie You encounter two natives of this…

Q: What's the answer for problem 16

A: it is given that, 13,10,7,5,7,7,2,4,3,2,3,15,4,4,2,8,7,8

Q: For each of the following problems, imagine that you are on a strange and unusual island, the…

A: Given - For each of the following problems, imagine that you are on a strange and unusual island,…

Q: Solve for the following word problem. 1. A train is leaving Divisoria on Monday late afternoon and…

A: We will solve this question using basic logic and arithmetic. We shall solve all the five parts of…

Q: Answer the following 4 following parts to the problem? Please explain how you recieve the varience…

A: Step 1: Click STAT and then ENTER Fill the values of x and p(x) click STAT again and then click…

Q: Given the problem

A: Given, utt=uxx+ux; 0<x<π, t>0 (1) u(0,…

Q: Hi, May you help me solve the attached problem (#25) wile showing the steps and answer? Thanks

A: Consider the given information: Operating cost per hour is $5132. Charge by each passenger is $100.…

Q: y+xy = xy3, y(1) = 2

Q: Hello, I am having trouble with section (c) and the last question for this problem

A: Solution:

Q: 2. BOOKS A book store bought 160 copies of a book from the publisher for $4,000. If the store gives…

A: 2. A book store bought 160 copies form the same book from a pubisher for 4,000.If the store gives…

Q: Solve the following problems. 1. A die is rolled once. Find the probablity that a). The number is…

A: Given: A die is rolled once. Number of outcomes =6

Q: Please only do parts d and e from the problem. I already have parts a b and

Q: my

A: Yes, your answer is correct.

Q: 1 1 2 1 1

A: Given, S = 1000, 0121, 0011, 010-1 Then we have to show whether S is Linearly dependent or…

Q: Given values for the following problems: ix, 1 1 2 4 35 48 59 6 11 7 14 8 17 9 18 10 20 1) 10 3) 4)…

A: Given

Q: Sp° In p dp р ар 10.

Q: I need some explanation on these 3 problems.

A: Since, we only answer up to 2 sub-parts, we will answer the first two. Please resubmit the question…

Q: Use the method of False Position to find solutions accurate to within 10−5 for the following…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Problem 7 Parts A and B please

A: To find first derivative , apply quotient rule

Q: Need help with #5 of attached problems. Thank you in advance

Q: Problem 2 Parts A, C, and D please

Q: Need answers for question 1. And question 2.

A: Given that: 1-Initial amount, a=$3000 rate of interest, r=3% Time period,…

Q: 18 problems and Andreas solved 13 problems. How many more problems has Ivan solved than Andreas?…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Can I have detailed explanation for parts (b) & (c) of the following question? Thank you!

A: Given, The number of printers sold weekly for each of the past 80 weeks. Number of printers sold…

Q: 4. E (6x + 6)°

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Question

Please write up proofs for the following problems. I need to answer them very clearly with step by step explant please ...Needed clear proof...Will be highly appreciated..Thank You

2. Let f: A –→ B and g: B → C be functions and suppose that gof: A → C is surjective. Prove that
g must be surjective and give an example to show that f need not be.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every subset T of A.
(See exercise 24.) Show that the relation f(x)Rg(x) if and only if f(x)=g(x) is an equivalence relation on R[ x ]. Describe the equivalence class [ f(x) ]. For each f(x)=i=0naixi in R[ x ], the formal derivative of f(x) is the polynomial f(x)=i=1niaixi1. (For n=0, f(x)=0 by definition.) Prove that [ f(x)+g(x) ]=f(x)+g(x). Prove that [ f(x)g(x) ]=f(x)g(x)+f(x)g(x).
18. Let and be defined as follows. In each case, compute for arbitrary . a. b. c. d. e.
For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions are correct. a. f(x)={ x2ifxiseven0ifxisodd b. f(x)={ 0ifxiseven2xifxisodd c. f(x)={ 2x+1ifxisevenx+12ifxisodd d. f(x)={ x2ifxisevenx32ifxisodd e. f(x)={ 3xifxiseven2xifxisodd f. f(x)={ 2x1ifxiseven2xifxisodd
Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.