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Prove that the functions are subsets.

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See the attached file.

14. Let f: A --> B, D is a subset of A, and E is a subset of B.

Prove that
a) f(f^-1(E)) is a subset of E
b) A - f^-1(E) is a subset of f^-1(B - E)
c) f^-1(B - E) is a subset of A - f^-1(E).
d) E = f(f^-1(E)) if E is a subset of Rng(f)

From Images of Sets. Prove for each part except (a) and (d) and explain each step of your solution.

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Solution Summary

Proofs for the images of sets problems (b), (c), (e) and (f) are provided in this solution in step-by-step format. This solution includes an attached Word file.

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