1. Let Js = {0, 1, 2, 3, 4}, and define functions f : J5 >/s and g : Js >/s as follows: For each x EJ5,: f (x)=(x+ 4) * mod 5 and g(x)=(x + 3x + 1) mod 5 Is f = g? Explain (1 pts) 2. Let A = {2, 3, 5} and B = {x, y}. Let p1 and p2 be the projections of A x B onto the first and second coordinates. That is, for each pair (a, b) E A x B, pi(a, b) = a and p2(a, b) = b: a. Find p1 (2, y) and p1(5, x). What is the range of p1 (1/2 pts)? b. Find p2 (2, y) and p2(5, x). What is the range of p2 (1/2 pts)? 3. Fill in the following table to show the values of all possible two-place Boolean functions. (1 pts). Input fif2 fa fa fs fo fife fo f 10 fil f12 f 13 f14 fis fic 4. Let X = {1, 5, 9} and Y = {3, 4, 7}. a. Define f: X -> Y by specifying that f (1) = 4, f (5) = 7, f (9) = 4 (1/2 pts). Is f one-to-one? Is f onto? Explain your answers b. Define g: X -> Y by specifying that g(1) = 7, g(5) = 3, g(9) = 4 (1/2 pts). 5. Let X = {1, 2, 3}, Y = {1, 2, 3, 4}, and Z = {1, 2}: a. Define a function f : X -> Y that is one-to-one but not onto (1/2pts). b. Define a function g: X -> Z that is onto but not one to- one (1/2pts)