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Prove: $f(f^{-1}(B))=B\cap f(X)$ if $f:X\rightarrow Y,A\subset X,B\subset Y$

$f(f^{-1}(B))=f(A)$

$Y=f(X)$

$f(A)=B\cap Y$

Is this correct?

user300045
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    No: (1) you haven't defined $A$ (it has to be $f^{-1}(B)$ for your first line to make sense, but you have to say so). (2) $f(X)$ may not equal all of $Y$, you can't assert this, and anyway it doesn't help. What you should do is: show that each of the two sets is $\subseteq$ the other. – BrianO Oct 20 '15 at 16:25
  • You might be interested in http://math.stackexchange.com/q/914957/11994 and its answers. – MarnixKlooster ReinstateMonica Oct 20 '15 at 16:53

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