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knowLittle
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Homework Statement
Prove that set of all onto mappings of A->A is closed under composition of mappings:
Homework Equations
Definition of onto and closure on sets.
The Attempt at a Solution
Say, ##f## and ##g## are onto mappings from A to A.
Now, say I have a set S(A) = {all onto mappings of A to A }, so ##f## and ##g \in S##
Then,
## f o g(a_0) = f(g(a_0)) = f(a_i) , a_i, a_0 \in A; a_i ## represents all elements in A that are being hitted.
Now, the domain of ##f## is set A, since ##g## is onto. And now all elements in the domain of ##f## will hit all elements in the codomain of f.
Therefore, ##fog \in S(A) ##
Is this correct? Or is it weak, illogical, flawed ... ?