Question 2 (3 points) =[G [ | Is the following statement true or false? 0 C {0} P ) True Yy () False Question 3 (3 points) =[G > | Is the following statement true or false? {0} 10} () a) True |:_:| ) False Question 4 (4 points) [ G [ | Let A and B be sets. Show that A U (A M B) _ A using a traditional verbal proof, a series of equalities that can be read forward and backward, or a membership table. You may type your work in the space below, or write it by hand and attach an image of your work to this question. Please use either .pdf or .jpg file types. Paragraph Question 5 (3 points) [ > Consider a finite universal set of a general nature (please do not specify). What subset of this universal set does the bit string with alf zeros represent? .~ Question 6 (3 points) E o] Listen u let U=1{0,1,2,3,4,5,6,7,.8 9}, A={2 3,4,5, 6} and B={0, 3, 6, 1. Find A N B, O a){0.1,2,4,5 7. 8,9 O v) 3, 6} o) 12,3, 4, 56,9 O d) 0,9 Question 7 (3 points) S @[> | let U=1{0,1,2,3,4,5,6,7,8 9, A={2 3, 4,5, 6L and B={0, 3, 6, 9. Find A - B. O a) 10, 9} O b) (3, 6} O o 11,78 O a) (2. 4, 51 Question 8 (4 points) =@ > What can we say about the sets A and B if we know that A M B A 2 (you may use words or symbols using the E button) Question 9 (4 points) Listen Determine whether the function f (ac ) = 4x - 1 where f : R -> Ris a bijection. If it is not, explain why not. Paragraph v BIUA V + v . .. Question 10 (4 points) Listen Determine whether the function f (2 ) - 3x2 + 2x - 5 where f : R -+ R is a bijection. If it is not, explain why not. Paragraph v B I UA Ev + v Question 11 (3 points) Listen Consider the function that assigns each positive integer to its FIRST (leading) digit. (For example, the positive integer 517 gets assigned to 5). In Blank 1: What is the domain of this function? In Blank 2: What is the range of this function? (note I am not asking for the co- domain here) Please use either the roster method or set-builder notation for your response. In Blank 3: Is this function injective? (yes or no) Blank # 1 A Blank # 2 Blank # 3 A/Question 12 (3 points) Listen Find f O f where f ( ac) = 3ac - 5 and f : R - R. Oa f(f(2)) = 9x2 - 30x - 25 Ob) f(f (a) ) = 3x -5 Oof(f ( 2) ) = 3x2 - 10 O d f(f(z)) = 9x - 20 Question 13 (3 points) Listen Find a pair of values (x, y) that serve as a counter-example for the statement that [xyl = [ac ] [y ] for all real numbers x and y. Question 14 (3 points) Listen List the first five terms of the sequence whose 7"" term is 3" - 2". Let n = 0, 1, 2, ... Question 15 (3 points) Listen Compute the summation: _ (2 + 2 ) (in case this is difficult to read, this is the summation from i = 0 to 4, of the sequence (i +2) ) O a) 2 O b) 20 O c) 10 O d) 8Question 16 (3 points) Listen Compute the summation: Eil (-2)i (in case this is difficult to read, this is the summation from i = 1 to 3 of the sequence (-2)^i ) O a) -4 O b ) - 6 O c) - 14 O d) 14