Needs some help with understanding the following

1)For A = {a, b, c} and B = {5, 10, 15, 20}.

a)How many elements are in A B?

b)List the elements of A B.

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.

(1,2) : 3(1) <2(2) + 5 = 3<9

b)Give two ordered pairs that do not belong to R.

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 a 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

3

5

6

4

2

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.

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.

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.