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Prove that the functions are subsets.

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)) iff 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.


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.