For problems 1-4, Let A = {1,2,3), B = {x,y,z,w), C = {0, p}, D =...

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For problems 1-4, Let A = {1,2,3), B = {x,y,z,w), C = {0, p}, D = {r,E,n} (1 2 3 1. Consider f: A → B given by ( x 3) zx a. Is f injective? Explain. Is f surjective? Explain. c. What is the range of f? b. d. What is f(2)? e. What is f-¹(x)? 1 2 3 2. Consider g: A → C given by (40) a. Is g injective? Explain. b. Is g surjective? Explain. c. What is the range of g? d. What is g(2)? e. What is g-¹(0)? 3. Consider h: C → D given by ( ) a. Is h injective? Explain. b. Ish surjective? Explain. c. What is the range of h? d. What is h(p)? e. What is h-¹(r)? 4. Give an example of a bijection between two of the four sets above. 5. Show that the set N X N is a countaby infinite set. For problems 1-4, Let A = {1,2,3), B = {x,y,z,w), C = {0, p}, D = {r,E,n} (1 2 3 1. Consider f: A → B given by ( x 3) zx a. Is f injective? Explain. Is f surjective? Explain. c. What is the range of f? b. d. What is f(2)? e. What is f-¹(x)? 1 2 3 2. Consider g: A → C given by (40) a. Is g injective? Explain. b. Is g surjective? Explain. c. What is the range of g? d. What is g(2)? e. What is g-¹(0)? 3. Consider h: C → D given by ( ) a. Is h injective? Explain. b. Ish surjective? Explain. c. What is the range of h? d. What is h(p)? e. What is h-¹(r)? 4. Give an example of a bijection between two of the four sets above. 5. Show that the set N X N is a countaby infinite set.