Question 5. Suppose f : A → B and g : X → Y are bijective functions. Let h : A × X → B × Y be a new function defined by h(a, x) = (f(a), g(x)). i) Prove that h is bijective. ii) Define the assignment rule for the inverse function h-1 : B × Y → A × X in terms of f-1 and g-1. (Recall: f-1: B → A and g-1 :Y → X exist since f and g are bijective.)

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