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About composite mapping

  • Thread starter Ka Yan
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  • #1
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Could anybody help me check whether my judgements ture or false? (MJ = My Judgement)

Suppose f maps A into B, and g maps B into C

1. If f and g are injective, then g[tex]\circ[/tex]f is injective;
(MJ)but that when g[tex]\circ [/tex]f is injective, the injectivity of f and g are unsure.

2. If f and g are surjective, then g[tex]\circ[/tex]f is surjective;
(MJ)and that when g[tex]\circ[/tex]f is surjective, f and g are both surjective.

Thx!
 
Last edited:

Answers and Replies

  • #2
HallsofIvy
Science Advisor
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What reasons do you have for those judgements? Can you think up a simple example where f and g are not injective but g[itex]\circ[/itex]f is? Try the case where A, B, and C have only a few members.
 

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