- 1 Let Js 0 1 2 3 4 And Define Functions F Jsjs And G Jjs As Follows For Each X Js F X X 4 Mod 5 A 1 (46.89 KiB) Viewed 57 times
1. Let Js = {0, 1, 2, 3, 4), and define functions f: JsJs and g: JJs as follows: For each x € Js,: f (x)=(x +4)* mod 5 and g(x)=(x² + 3x + 1) mod 5 Is f = g? Explain (1 pts) 2. Let A = {2, 3, 5) and B = {x, y). Let p, and p₂ be the projections of A x B onto the first and second coordinates. That is, for each pair (a, b) EA x B, p₁(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 fi fa fa fa Ja Ja Ja Ja Jo f10 f11 12 13 14 15 16 J₂JSJ 0 01 00 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 fone-to-one? Is fonto? 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).