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Sorry, but I'm in dire need(Proofs)

by QuantumDefect
Tags: dire, needproofs
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QuantumDefect
#1
May16-06, 12:28 AM
P: 62
Hello, I need some help. Could someone kick me(hard please) in the right direction here? Here are the statements I need to prove:
1) If g of f is injective, then f is injective
2) If g of f is subjective, then g is subjective

where g and f are functions where f:A->B and g:B -> C where A,B and C are sets

Any kicks in the right direction would be GREATLY appreciated. Thank you.
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#2
May16-06, 12:56 AM
P: 304
Both can be done easily by contradiction.
Curious3141
#3
May16-06, 01:02 AM
HW Helper
Curious3141's Avatar
P: 2,943
Start with the definitions of injections and surjections (note the spelling of the latter), and draw functional mappings (domain/codomain diagrams). The proof is fairly easy from inspecting the mappings.

Wikipedia has fairly good pages on these subjects, complete with the mappings you need for the proof : http://en.wikipedia.org/wiki/Injective_function

http://en.wikipedia.org/wiki/Surjection


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