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Let f: X-->Y be a function from one set X to another set Y, let S be a subset of X, and let U be a subset of Y. What in general can one say about f^-1(f(S)) and S? What about f(f^-1(U)) and U?

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Let f: X-->Y be a function from one set X to another set Y, let S be a subset of X, and let U be a subset of Y. What in general can one say about and f^-1(f(S)) and S? What about f(f^-1(U)) and U?

We know that f(S) denotes the set of the images of all elements of S under the function f.
So, f(s) = {b element of Y/ f(a) = b, for some a element of S}

Similarly f^-1(b) = {a element of S/f(a) = b, b element of Y} indicates the set of all elements of S that are mapped to some element b in Y through f.

Let us see two examples ...

#### Solution Summary

This solution explains how to provide proof for the given functions.

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