# Prove the the function of the union of two sets

Theorem 4.16

Let f: A --> B, C and D be subsets of A, and E and F be subsets of B. Then

b) f(the union of C and D) = the union of f(C) and f(D)

d) f^-1(the union of E and F) = the union of f^-1(E) and f^-1(F).

See the attached file.

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#### Solution Summary

This is a proof regarding functions, intersections, and subsets provided in an attached Word document.

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Proof about Functions

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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