Inverse image. For the following functions f: X Y and SCY deter- mine f-(S): (a) f:...

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Inverse image. For the following functions f: X→ Y and SCY deter- mine f-¹(S): (a) f: R2R given by f(x, y) = x² - y² and S = [0, 1]. (b) X a finite set and f: 2x x 2X → 2X given by f(A, B) = An B and S = {X}. (c) f: Q² Q2 given by f(x, y) = (2x - y, -x + y) and S = (2, 3). 3. Prove that for any subset SC X of a set X we have 15¹({1}) = S. What is 1¹({0})? Inverse image. For the following functions f: X→ Y and SCY deter- mine f-¹(S): (a) f: R2R given by f(x, y) = x² - y² and S = [0, 1]. (b) X a finite set and f: 2x x 2X → 2X given by f(A, B) = An B and S = {X}. (c) f: Q² Q2 given by f(x, y) = (2x - y, -x + y) and S = (2, 3). 3. Prove that for any subset SC X of a set X we have 15¹({1}) = S. What is 1¹({0})?

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The detailed answer for the above question is provided below a fS x2 y2 x y S x2 y2 x y 0 1 1 0 1 b ... View the full answer