Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let g: A → B and f:B → C Prove that g is one-to-one if f og is one-to-one

Let g: A → B and f:B → C Prove that g is one-to-one if f og is one-to-one

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

 

a.) Explain in your own words what the proof allows you to assume and requires you to show.

b.) Provide 2-3 examples to demonstrate the statement is true or false.

c.) Explain the meaning of any notation used in the problem and in your solution.

d.)Logically valid proof supported with justification.

Let g: A → B and f:B → C Prove that g is one-to-one iffogis one-to-one
Transcribed Image Text:Let g: A → B and f:B → C Prove that g is one-to-one iffogis one-to-one
Expert Solution
Step 1

Given g:A→B and f:B→C be two map.

We have to prove that g is one-one if fοg is one-one.

Definition of one-one function:- Let f:X→Y be any function the f is said to be one-one if ∀a,b∈X such that a≠b

⇒fa≠fb

Since, fοg is defined as fοg:A→C

Since, Given fοg:A→C is one-one

Then ∀x,y∈A such that x≠y

⇒fοgx≠fοgy⇒gx≠gy

This implies that g is one-one.

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Logical Arguments
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS