Final answer:
Set A consists of the even counting numbers less than 14 and is represented in roster form as A = {2, 4, 6, 8, 10, 12}. The sample space S includes all whole numbers starting at one and less than 20. The intersection of set A and set B, which is greater than 13, results in A AND B = {14, 16, 18}.
Step-by-step explanation:
To write set A using the roster method, we list all the even counting numbers less than 14: A = {2, 4, 6, 8, 10, 12}. The roster method involves writing all the elements of the set within curly braces, separated by commas.
The sample space S includes all whole numbers from 1 up to but not including 20: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}. Event A is all even numbers in S, which are A = {2, 4, 6, 8, 10, 12, 14, 16, 18}, and event B is numbers greater than 13, which are B = {14, 15, 16, 17, 18, 19}. Set A AND B refers to the numbers that are present in both A and B, hence A AND B = {14, 16, 18}.