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If f:X→Y is onto and g:Y→Z is onto,then prove that gof:X→Z is onto.

If f:X→Y is onto and g:Y→Z is onto,then prove that gof:X→Z is onto.

Grade:12th Pass

3 Answers

jitender lakhanpal
62 Points
9 years ago

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        

hence proved

 

 

 

 

 

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Aman Bansal
592 Points
9 years ago

Dear Menka,

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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Ashwin Muralidharan IIT Madras
290 Points
9 years ago

 

Hi Menka,

 

The solution is written in the scanned copy.

Hope that helps.

 

All the best,

Regards,

Ashwin (IIT Madras).

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