home > q&a board > other > topic: number theory2134r

Q BgQuestion:

Apprentice
Karma Points: 114
Respect (100%):
posted by  ProEliteMark on 9/11/2008 12:38:50 PM  |  status: Live  

number theory2134r

Course Textbook Chapter Problem
N/A N/A N/A N/A
Question Details:
Suppose that F1 ο G2 =F1 ο G1  then  F : S→ T, G1 : T → U, G2 : T →U,. Define a function  F : R2 ? R2 by F(x, y) = (x + y, x - y).  . Show that if F is onto, Suppose that G1 ο F = G2 ο F. Show by counterexample that if F is not onto then  show that if H is one-to-one, then G1 = G2. But this means one of two things,  H is not one to one, and if and only if

AAnswers:

Answer Question
(Cramster SME)
Moderator
posted by James(SME-Math) on 9/12/2008 12:41:44 AM  |  status: Live
Asker's Rating: Lifesaver   
ProEliteMark's comment:
"thank for all of them,. lol"
Response Details:
a)
H o G1 = H o G2
 
Suppose that H is one - to -one
 
To show that  G1 = G2
 
Let  tT.
 
Now H o G1(t) = H o G2(t)
 
=> H (G1(t))  = H( G2(t))
 
=> G1(t) = G2(t)       (since H is one - to -one)
 
=> G1 = G2
Hope this helps you..... 
Apprentice
Karma Points: 190
posted by iceberge on 10/20/2008 10:16:55 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
F1 ο G1  then  F : S→ T, G1 : T → U, G2 : T →U,. Define a function  F : R2 ? R2 by F(x, y) = (x + y, x - y).  . Show that if F is onto, Suppose that G1 ο F = G2 ο F. Show by counterexample that if F is not onto then  show that if H is one-to-one, then G1 = G2. But this means one of two things,  H is not one to one, and i
Apprentice
Karma Points: 113
posted by Allie Boy on 10/20/2008 10:22:39 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
F1 ο G1  then  F : S→ T, G1 : T → U, G2 : T →U,. Define a function  F : R2 ? R2 by F(x, y) = (x + y, x - y).  . Show that if F is onto, Suppose that G1 ο F = G2 ο F. Show by counterexample that if F is not onto then  show that if H is one-to-one, then G1 = G2. But this means one of two things,  H is not one to one, and i
Answer Question
Ask New Question

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today » How Cramster is different than tutoring »

Need Help In

Useful Links