(a) Show that if I: A -+ B is injective and E ~ A, then 1-1(f(E = E. Givean example to
Chapter 1, Problem 17(choose chapter or problem)
(a) Show that if I: A -+ B is injective and E ~ A, then 1-1(f(E = E. Givean example to show that equality need not hold if I is not injective. (b) Show that if I : A -+ B is surjective and H B, then I (f-l (H = H. Givean example to showthat equalityneednot holdif I is notsurjective. 1
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