Question: (a) Show that if f : A B is injective and E A, then f-1( f (E)) = E. Give an example to

(a) Show that if f : A → B is injective and E ⊂ A, then f-1( f (E)) = E. Give an example to show that equality need not hold if f is not injective.
(b) Show that if f : A → B is surjective and H ⊂ B, then (f-1(H)) = H. Give an example to show that equality need not hold if f is not surjective.

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