I need help understanding the following problem:
Let A and B be nonempty subsets of R and let f:A->B be a function. If C \contained in A and D\contained in B, which of the following must be true?
(A) C \contained_in f^(-1)(f(C))
(B) D \contained in f(f^(-1)(D))
(C) f^(-1)(f(C)) \contained in C
(D) f^(-1)(f(C)) = f(f^(-1)(D))
(E) f(f^(-1)(D)) = f^(-1)(D)
I understand why A is true, but I don't understand why B is not true. Or perhaps any of you could point me to some part of an analysis textbook or an intro book that states the rules that help you figure out the right answer for this problem.