Problem 2 Decide with proof whether the following are well-defied functions. 1. Let I = {0, 1, 2, 3, 4}. Define the indexed family of sets Xi = {i + 5n : n Z}, for all i I. Notice that the family {Xi}iI is the set {X0, X1, X2, X3, X4}. The function in question is f : {Xi}iI Z where f (Xi) = a such that a Xi, for all i I.

2. h is a function whose graph is given by Gr(h) = {(x, y) R R : x2 + y2 = 1}

3. Let Y = {Q, R \ Q}. Y has the set of rational numbers and the set of irrational numbers as the two elements of it. Define g : R Y where, for all x R, g(x) is a set in Y such that x g(x) Prove if well-defined. Provide counter example if that's not possible