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posted by  Sam the Plumber on 9/11/2008 12:44:40 PM  |  status: Live  

number theory2134r

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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

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posted by WSAN on 9/11/2008 8:11:38 PM  |  status: Live
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Sam the Plumber's comment:
"hey so far this is the best one,, the diagram really help thank you..,"
Response Details:
a) H is one to one.
to show  if  H o G1 = H o G2 then G1 = G2 , consider
(Ho G1)(x) =(H o G2) (x)
i.e. H( G1( x )) = H ( G2( x)) ==>
==>  G1(x) = G2(x)  for all x in T. ( since H is one-one )
 
==> G1 = G2
 
b)  
H o G 1 = { ( a,β), ( b , α) ,( c, α) } = H o G2
but from the diagrams we can easily follow that G1 G2.
 
SWAN
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posted by iceberge on 10/20/2008 9:59:56 AM  |  status: Live
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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
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