SOLUTION: MAT 230 Southern New Hampshire University Module 6 Discrete Mathematics HW

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MAT 230 Module Six Homework General: • Before threshold this homework, be enduring to learn the texteffort sections and the material in Module Six. • Type your defenses into this muniment and be enduring to profession all steps for arriving at your solution. Just giving a latest sum may not admit generous reputation. • You may observation and paste prosaic symbols from the statements of the questions into your defense. This muniment was engenderd using the Arial Unicode font. • These homeeffort examples are proprietary to SNHU COCE. They may not be posted on any non-SNHU website. • The Institutional Release Statement in the way shell confers details about SNHU’s use of systems that collate tyro submissions to a database of online, SNHU, and other universities’ muniments. SNHU MAT230 Page 1 of 6 Module Six Homework 1) For A = {a, b, c, d, e} and B = {yellow, orange-flame, sky cerulean, untried, unblemished, red, black}. a) Define a reference R from A to B that is a exercise and contains at smallest 4 disposeed pairs. b) What is the lordship of this exercise? c) What is the class of this exercise? This example is harmonious to Example 2 and to Exercises 1 and 2 in Section 5.1 of your SNHU MAT230 textbook. 2) Define exercises f: ℝ → ℝ and g: ℝ → ℝ by f(a) = 2 + a and g(b) = 3b – 1. Find the subjoined, showing the steps to get to your defense. a) (f ○ g) (0). b) (g ○ f) (1). c) (f ○ g) (x). d) (g ○ f) (x). This example is harmonious to Example 9 and to Exercises 9 and 10 in Section 5.1 of your SNHU MAT230 textbook. 3) Let A = {CA, NH, IL, OH, SC, WV, PA, TX} and B = {book, consideration, chair, fork, thoroughfare, car}. Using at smallest 5 disposeed pairs, individualize the subjoined: a) Define a exercise f from A to B that is one-to-one. b) Define a exercise g from A to B that is not one-to-one. c) Define a exercise h from A to B that is onto. d) Define a exercise α from A to B that is not onto. e) Define a exercise β from B to A that acts as the inverse of the exercise f that you created in portio a) of this example. This example is harmonious to Examples 10–12 and to Exercises 11 and 12 in Section 5.1 of your SNHU MAT230 textbook. SNHU MAT230 Page 2 of 6 Module Six Homework 4) The exercise f: ℝ → ℝ defined by f(x) = 7x is onto accordingly for any veritable sum r, we own that r/7 is a veritable sum and f(r/7) = r. Consider the identical exercise defined on the integers g: ℤ → ℤ by g(n) = 7n. Explain why g is not onto ℤ and confer one integer that g cannot output. This example is harmonious to Examples 10–12 and to Exercises 13–17 in Section 5.1 of your SNHU MAT230 textbook. 5) Let f: ℝ → ℝ be the exercise f(x) = x3 – 1. Find f–1 (x) and fulfill that it is the inverse of f. This example is harmonious to Examples 16 and 17 and to Exercises 20–22 in Section 5.1 of your SNHU MAT230 textbook. 6) Suppose a sanity prophylactic guild identifies each portion after a while an 8-digit fidelity number. Define the hashing exercise h that earliest takes the earliest 3 digits of an fidelity sum as one sum and the decisive 5 digits as another sum, then adds them, and decisively applies the mod–37 exercise. This example is harmonious to Example 10 and to Exercises 24–26 in Section 5.2 of your SNHU MAT230 textbook. a) How sundry incorporateed lists does this engender? b) Compute h(59243973). c) Compute h(42280135). 7) Compute the stay digit c for the 10-digit ISBN codes underneath. Profession the calculations that you used to gain your defenses. This example is harmonious to Exercise 49 in Section 5.2 of your SNHU MAT230 textbook. a) 0-523-76952-c (the judicious 0 indicates that this is an English effort) b) 2-426-25967-c (the judicious 2 indicates that this is a French effort) 8) The draw underneath professions the graph of f(x) in red and the graph of b(x) in sky cerulean. Does the graph profession that r is O(b), or that b is O(r), twain, or neither? Explain your defense. SNHU MAT230 Page 3 of 6 Module Six Homework This example is harmonious to Example 5 and to Exercise 11 in Section 5.3 of your SNHU MAT230 textbook. 9) Define a reference R on the set of assured veritable sums by (x, y) ∈ R if and singly if x2 – y2 = 0. Determine if the reference R is a portioial dispose. If it is not a portioial dispose, explain which peculiarity or properties R fails to own. This example is harmonious to Example 5 and to Exercises 1–3 in Section 6.1 of your SNHU MAT230 textbook. 10) Determine the disposeed pairs in the reference resolute by the Hasse diagram underneath on the set A = {a, b, c, d, e}. Engender the matrix fidelity of this poset. This example is harmonious to Example 11 and to Exercises 11 and 12 in Section 6.1 of your SNHU MAT230 textbook. SNHU MAT230 Page 4 of 6 Module Six Homework 11) Define U = {1, 2, 3, 4, 5}. Consider the subjoined subsets of U: A = {1, 2}, B = {3, 4, 5}, C = {1, 2, 5}, D = {5} You may use (copy/paste/move/resize/etc.) the images underneath to engender your graph. This example is harmonious to Example 12 and to Exercises 21–24 in Section 6.1 of your SNHU MAT230 textbook. a) Engender the Hasse diagram using ⊆ as the portioial dispose on the sets A, B, C, D, U, and . b) Is this a rectirectilinear dispose? Explain your defense. A B C D U ∅ 12) If ≺ represents lexicographic dispose, then which of the subjoined is/are penny? Explain your answers. This example is harmonious to Example 9 and Exercises 19 and 20 in Section 6.1 of your SNHU MAT230 textbook. a) (3, 11) ≺ (3, 0) b) (4, 7) ≺ (2, 17) c) (6, 2) and (8, 1) are not resembling accordingly we scarcity the earliest sum to be larger in one of the pairs. 13) Let B = {2, 3, 4, 6, 12, 24, 36} and R be defined by xRy if and singly if x|y. This example is harmonious to Exercise 49 in Section 5.2 of your SNHU MAT230 textbook. SNHU MAT230 Page 5 of 6 Module Six Homework a) Determine all minimal and all maximal elements of the poset. b) Find all smallest and principal elements of the poset. Explain your defenses. This example is harmonious to Examples 1–3 and 5–7 and to Exercises 8 and 16 in Section 6.1 of your SNHU MAT230 textbook. SNHU MAT230 Page 6 of 6 Module Six Homework Formula Sheet In this way you are expected to profession your effort for your assignments. To do so, you must profession the formulas and equations used. Equation Editor (Equation Tools/Equation Ribbon) from Microsoft Operation is one careless implement you can use. For tutorials, use the subjoined resources: Microsoft Word 2007 and 2010:  http://office.microsoft.com/en-us/word-help/where-is-equation-editor-HA001230366.aspx  https://www.youtube.com/watch?v=lUqxmSue7Fo Microsoft for Mac:  Insert>>Object>>Microsoft Equation   https://support.office.com/en-us/article/Insert-or-edit-an-equation-or-expression-2878ad404162-4231-8e8a-4fe0e6fc5358 http://www.dummies.com/how-to/content/writing-and-editing-equations-in-office-2011-form.html Below are some premade templates that were engenderd using Equation Editor that you may find helpful when completing your homework. Sets 𝑈 = {𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓, 𝑔} _______ ∈ 𝐶 _____ ∉ 𝐶 {𝑥|𝑥 ∈ ℤ } 𝐴⊆𝑈 𝐵⊆𝑈 Α∩Β 𝐶 ∪Β 𝐴∪𝐵−𝐶 𝐴⨁𝐵 (𝑥, 𝑦)  𝑅   Logic and Truth Tables ~ ∧ ∨ 𝑝→𝑞 ← 𝑃(𝑥) ∃ ∀ ∀𝑛 𝑃(𝑛), ∃𝑛 𝑃(𝑛) (𝑝⋁𝑞)⋀ 𝑝 ∴ 𝐴 = ℤ > Purchase defense to see generous attachment

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