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If f:X→Y is onto and g:Y→Z is onto,then prove that gof:X→Z is onto.
Dear Menka,
in order to prove that gof:X→Z is onto we have to show that every element in Z
has it's pre image in X i.e
if C be an arbitrary element of Z,B be an arbitrary element of Y, A be an arbitrary element of Z.
for all C belongs to Z there exists A belongs X such that (gof)(A)=C ------------to prove
as f:X→Y is onto that means f (A) = B-------------------1
g:Y→Z is onto that means g (B) = C ----------------------2
from 1 & 2 we get
gof(A) = g(f(A))=g(B) = C
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jitender
askiitians expert
Assume an element x1 since x,y and y,z are onto we can prove that x,z is also onto.
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Thanks
Aman Bansal
Askiitian Expert
Hi Menka,
The solution is written in the scanned copy.
Hope that helps.
All the best,
Regards,
Ashwin (IIT Madras).
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