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May 23rd, 2014, 07:54 AM   #1
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image and inverse image

f : X → Y and A,B subsets of X and Y.


I can't see why f(f −1(B)) ⊆ B and not f(f −1(B)) = B in all cases. Can someone help ? I would like to see it with Venn diagram and with a proof.
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May 23rd, 2014, 12:27 PM   #2
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This happens when $B\setminus\text{image}(f)\ne\emptyset$.
Evgeny.Makarov is offline  
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