IST 230 Quiz Lessons 4 - 5 - Questions are worth 10 points each Chapter 4 1. Evaluate the following logical expression with x = y = 0 and w = z = 1. z x + ( 1+wy ) 2. Give a Boolean expression, specified by the input/output table, for the function f(x,y,z). Use the sum of minterm expression described in the text. x y z f(x,y,z) 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 3. Suppose x, y, and z are Boolean variables. Explain why the following expression is or is not in Disjunctive Normal Form (where juxtaposition is used to indicate Boolean multiplication): ( x+ y+ z ) ( z+ xyz ) Chapter 5 4. Draw the arrow diagram and the matrix representation for the following relation on the set {1, 2, 3, 4}: R = { (1,3), (1, 4), (2, 1), (3,2), (3, 4), (4,2)}. 5. Suppose A = {1, 2, 3, 4}. Let S and R be relations on A defined as follows: S = { (1, 1), (1, 3), (2, 3), (3, 4), (4,1) } R = { (1, 4), (2, 2), (3, 2), (4, 2) } a. Explain why the ordered pair (1,2) is or is not in the relation S o R. b. Explain why the ordered pair (2,3) is or is not in the relation S o R. 6. The table below shows the database of vehicles on a used car lot. It's actually just a portion of the list, but for the purposes of this question, assume it lists all the vehicles. Category Sedan Truck SUV Sedan Sedan Minivan Sedan Make Chevrolet Ford Ford Toyota Honda Honda Chrysler Color Yellow Black Silver Maroon Blue Blue Red Year 2008 2013 2013 2003 2002 2010 2014 a. Give a key for this database. b. Show the results of the operation SELECT[Category ="Sedan" ^ Year > "2008"]. c. Show the results of the operation PROJECT[Color]. d. Show the results of the operation SELECT[Make = "Ford"] followed by PROJECT[Color]. Express in English what question this combination of queries is asking. e. What operation or operations should be performed if you wanted to know which vehicles were made by Honda and made after 2005? 7. Suppose A = {1, 2, 3}, and suppose the relation R on A is defined by R = { (1,1), (1,2), (2,3), (3,3) }. List as a set of ordered pairs the transitive closure of R. IST 230 Quiz Lessons 6 - 8 - Questions are worth 10 points each Chapter 6 1. Write an algorithm in pseudo-code with the following input and output. Input: a sequence of n integers a1, a2,..., an. Output: The sum of the squares of the integers in the sequence. 2. What is the value of count after the last iteration of the outer for loop? Be sure to show your work. count :=0 For i= 1 to 2 For j=1 to 3 count :=j(count + 2i) End-for End-for Chapter 7 3. Find the next three terms (a2, a3, and a4) of the following sequence: a1 = 2, and for all integers k > 1, ak = ak-1 - 3k. 4. Prove using mathematical induction that 1 1 1 n + + ...+ = forallintegersn 1 . 12 23 n ( n+ 1 ) n+1 Chapter 8 5. Explain why 4 is or is not a multiplicative inverse mod 10 of 7. 6. Find the values for each of the following: a. 3 times 5 in Z 10 b. 3 times 5 in Z 5 c. 3 times 5 in Z 3 d. 5 + 5 in Z 5 e. 5 + 3 in Z 10 7. Perform the following conversions a. Convert 1100 0100 1010 00112 to hexadecimal. b. Convert 10001112 to decimal. c. Convert 0xF7A4B1 to binary