Let f : A → B and let X,Y be subsets of the domain A. For any Z ⊆ A, define the image of Z under f to be the set f[Z] = {b ∈ B|∃z ∈ Z(f(z) = b)}. a. Show that f[X ∪Y] = f[X]∪f[Y]. b. Give an example of a function f and subsets X,Y of its domain to show that it is not always true that f[X ∩Y] = f[X]∩f[Y].

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Question ID: mtid-5-stid-8-sqid-4070-qpid-2769