MAT 230 Module Five Homework General: Before beginning this homework, be sure to read the textbook sections and the material in Module Five. Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. You may copy and paste mathematical symbols from the statements of the questions into your solution. This document was created using the Arial Unicode font. These homework problems are proprietary to SNHU COCE. They may not be posted on any non-SNHU website. The Institutional Release Statement in the course shell gives details about SNHU's use of systems that compare student submissions to a database of online, SNHU, and other universities' documents. SNHU MAT230 Page 1 of 3 Module Five Homework 1) For A = {a, b, c} and B = {5, 10, 15, 20}. a) How many elements are in A B? 3*4=12 b) List the elements of A B. A*B {(a,5), (b,5), (c,5), (a,10), (b,10), (c,10), (a,15), (b,15), (c,15), (a,20), (b,20), (c,20)} This problem is similar to Example 4 and to Exercises 5-7 in Section 4.1 of your SNHU MAT230 textbook. 2) Let A = +, the positive integers, and let R be the relation defined by a R b if and only if 3a < 2b + 5. a) Give two ordered pairs that belong to R. (10,5), (8,2) b) Give two ordered pairs that do not belong to R. (1,1) (2, 10) This problem is similar to Examples 3 and 4 and to Exercises 1-3 in Section 4.2 of your SNHU MAT230 textbook. 3) Let A = {1, 2, 3, 4, 5, 6} = B. Define a relation R as a R b if and only if a + b < 6. Find the domain, range, matrix representation of R, and the digraph of R. You may use (copy/paste/move/resize/etc.) the images below to create your graph. This problem is similar to Examples 11, 19, and 23 and to Exercises 10-12 in Section 4.2 of your SNHU MAT230 textbook. 1 2 3 4 5 6 4) Determine whether the relation R defined below is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. For each property, either explain why R has that property or give an example showing why it does not. a) Let A = {1, 2, 3, 4} and let R = { (2, 3) } b) Let A = {1, 2, 3, 4} and let R = { (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 4) }. This problem is similar to Examples 1, 4, and 10 and to Exercises 1-4, 7, and 8 in Section 4.4 of your SNHU MAT230 textbook. 5) Let A = {1, 2, 3, 4, 5} and R be the relation on the set A whose digraph is shown below. Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. For each property, either explain why R has that property or give an example showing why it does not. This problem is similar to a combination of Example 23 in Section 4.2 with Example 6 in Section 4.4, and to Exercises 9 and 10 in Section 4.4 of your SNHU MAT230 textbook. SNHU MAT230 Page 2 of 3 Module Five Homework 6) Let A = {1, 2, 3, 4, 5} and R be the relation on the set A whose matrix is shown below. Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. For each property, either explain why R has that property or give an example showing why it does not. This problem is similar to Examples 6 and 11 and to Exercises 11 and 12 in Section 4.4 of your SNHU MAT230 textbook. 1 1 M = 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 7) Let A = and R be the relation on A where a R b if and only if a + b is a multiple of 4. Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. For each property, either explain why R has that property or give an example showing why it does not. This problem is similar to Examples 5 and 9 and to Exercises 13-19 in Section 4.4 of your SNHU MAT230 textbook. SNHU MAT230 Page 3 of 3 Module Five