3. Suppose that X and Y are two sets and f: X → Y is a function. Prove each of the following: (i) If A and B are two subsets of X and A C B, then ƒ(A) C ƒ(B). (ii) If {Hala e A} is an indexed family of subsets of X, then f(UaEAHa) = Uae^ƒ (Ha). (iii) If {Gala e A} is an indexed family of subsets of Y, then f-¹ (naEAGα) = nae^ f-¹(G₁).

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