I am issues with proving the following problem: $f^{-1}(f(A)) ⊃ A$

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Yes, the intended meaning is what you're thinking.

Now, an element $x$ belongs to $f^{-1}(B)$ if and only if $f(x)\in B$. Take $a\in A$: can you say that $f(a)\in f(A)$?

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mathguy
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Updated on September 04, 2022

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  • mathguy
    mathguy about 1 year

    I am unsure as to where to start with this problem. The way I read it is that $f^{-1}(f(A)) ⊃ A$ means that $A$ is a subset of the preimage of the image of $A$. But I am unsure.