2.1 Set Concepts 45 Solution From the table we can see that set M {Williams College, Amherst = College, Wellesley College, Bowdoin College, Carleton College, United States Naval Academy}. ■ Solution a) { } ∈ blue orange, yellow, blue, green is a true statement since blue is an element of the set { } orange, yellow, blue, green . b) { } ∈ peppermint spearmint, cinnamon, licorice is a false statement since peppermint is not an element of the set { } spearmint, cinnamon, licorice c) { } { } ∈ sapphire gold, diamond, ruby, sapphire is a false statement because { } sapphire is a set and the set { } sapphire is not an element of the set { } gold, diamond, ruby, sapphire . ■ Now try Exercise 57 Example 8 National Liberal Arts Colleges The following table shows the rankings, according to U.S. News & World Reports, for the top ten national liberal arts colleges in the United States for the year 2022. The locations of the colleges are also given. Let set M be the set of colleges given in the table that are in states that begin with the letter M. Write set M in roster form. Now try Exercise 75 m The United States Naval Academy Rank College Location 1 Williams College Williamstown, MA 2 Amherst College Amherst, MA 3 Pomona College Claremont, CA 4 Swarthmore College Swarthmore, PA 5 Wellesley College Wellesley, MA 6 Bowdoin College Brunswick, ME 7 Carleton College Northfield, MN 8 United States Naval Academy Annapolis, MD 9 Claremont McKenna College Claremont, CA 10 United States Military Academy at West Point West Point, NY Fundamental Set Concepts A set is said to be finite if it either contains no elements or the number of elements in the set is a natural number. The set { } = B 2, 4, 6, 8, 10 is a finite set because the number of elements in the set is 5, and 5 is a natural number. A set that is not finite is said to be infinite. The set of counting numbers is one example of an infinite set. Infinite sets are discussed in more detail in Section 2.6. Example 9 Finite and Infinite Sets Determine whether each set is finite or infinite. a) { } = A 1, 4, 7, 10, 13, 16 b) { } = … B 1, 4, 7, 10, 13, 16, c) C is the set of all natural numbers between 1 and 1,000,000, inclusive. d) D is the set of all fractions between 0 and 1. Source: USNews.com Kayla1017/Shutterstock
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