Module One Homework General: Before beginning this homework, be sure to read the textbook readings and the module notes. For additional practice, each homework problem has some ungraded examples and sample problems from the text that you can review, and they directly correspond with your graded homework. Work on those problems if needed, and post your questions to this week's ungraded discussion forum. Work within this document for your homework, and be sure to show all steps for arriving at your solution. 1 Section 1.1 Homework 1) Suppose C = {red, blue, gray, orange}. For a) and b) below, fill in the value(s) that makes the statement true (Note: More than one answer is possible). This problem is similar to example 1 and problems 1.1.1 and 1.1.2. a) _____ b) _____ 2) List the elements of the set examples 2 and 5 and problem 1.1.4. . This problem is similar to 3) Consider U = {2, , , }, A={a, , }, and B={2, }. Complete parts a) and b) below. This problem is similar to examples 3, 7, and 8 and problems 1.1.15 and 1.1.16. a) Is ? Explain why. b) Is ? Explain why. 2 Section 1.2 Homework 1) Consider the following sets: U = {pink, purple, red, blue, gray, orange, green, yellow, indigo, violet} A = {orange, purple, red, yellow} B = {blue, gray, orange} C = {pink, violet, red} Compute each of the following: a) b) c) d) e) = = = = = This problem is similar to examples 1, 2, 4, and 6 and problems 1.2.1-1.2.4. 2) The records of 200 SNHU students show the following courses taken: 104 students took Latin 103 students took Greek 35 students took Sanskrit 46 students took Latin and Greek 24 students took Greek and Sanskrit 9 students took all 3 28 students took none of these languages How many students took only Greek? How many students took Latin and Sanskrit, but not Greek? Review Theorem 3. This problem is similar to example 10 and problems 1.2.25-1.2.28. 3 Section 1.3 Homework 1) Give the set corresponding to the sequence: yabbadabbadoo. This problem is similar to examples 3, 9, and 11 and problems 1.3.1-1.3.4. 2) Consider the sequence defined by an = n (n+1) . 2 Is this a recursive or explicit equation? Explain why. Using the formula, list the first 4 terms of the sequence (starting with n=1). This problem is similar to examples 4-7 and problems 1.3.7-1.3.14. 3) Consider the sequence defined by a1 = 2 and an = 2 - an-1. Is this a recursive or explicit equation? Explain why. Using the formula, list the first 4 terms of the sequence (starting with n=1). This problem is similar to examples 4-7 and problems 1.3.7-1.3.14. 4) Consider the following sets: U = {pink, purple, red, blue, gray, orange, green, yellow, indigo, violet} A = {orange, purple, red, yellow} B = {blue, gray, orange} C = {pink, violet, red} Represent each of the following with an array of zeros and ones: a) = b) = c) = 4 This problem is similar to examples 12 and 13 and problems 1.3.26 and 1.3.27. Section 1.5 Homework Answer problems 1-3 using the following matrices: A= [ 1 2 1 2 0 2 B= [ ] 2 0 2 1 1 1 0 2 0 1) Identify the following values: a13 = , a21 = , b12 = , b21 = This problem is similar to example 1 and problem 1.5.1 parts a, b, and c. 2) Compute A + A. This problem is similar to example 5 and problem 1.5.5 part a. 3) Of AB and BA, only one product is defined. Explain which product is undefined and why. Evaluate the product that is defined. This problem is similar to example 7 and problem 1.5.5 part b. 5 6