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December 6th, 2007, 12:15 PM  #1 
Newbie Joined: Dec 2007 Posts: 4 Thanks: 0  compostion and injectivity
I need help with the following problem... If the composition function g compose f : A> C is an injection, then the function f : A>B is an injection. 
December 6th, 2007, 01:15 PM  #2 
Member Joined: Nov 2007 Posts: 50 Thanks: 0  Re: compostion and injectivity 
December 6th, 2007, 01:37 PM  #3 
Newbie Joined: Dec 2007 Posts: 4 Thanks: 0 
Great! Thanks a lot! Now... how about this one If the composition function g compose f: A> C is an injection, then the function g : B>C is an injection. 
December 6th, 2007, 01:42 PM  #4  
Member Joined: Nov 2007 Posts: 50 Thanks: 0  Quote:
Example: f: {0}>{0,1} f(0)=0 g: {0,1}>{0,1} g(0)=g(1)=0 Their composition is h: {0} > {0,1} h(0)=0. Note that the composition is injective, but g is not injective. In case you wanted to write surjective instead of injective, the proof can be found again at planetmath.  
December 6th, 2007, 01:48 PM  #5 
Newbie Joined: Dec 2007 Posts: 4 Thanks: 0 
Nah, that's what the problem stated. However the prompt was "prove or disprove", so I'll just use a counterexample. Could you maybe explain yours a little further?


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