R 1 Sets Basic Definitions Operations on Sets

R. 1 Example 1 Using Set Notation and Terminology (page 2) Identify each set as finite or infinite. Then determine whether 8 is an element of the set. (a) {5, 6, 7, …, 10} finite; 8 is an element. (b) infinite; 8 is not an element. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 2

R. 1 Example 1 Using Set Notation and Terminology (cont) Identify each set as finite or infinite. Then determine whether 8 is an element of the set. (c) {x |x is a fraction between 9 and 10} infinite; 8 is not an element. (d) {x | x is a natural number between 7 and 9} finite; 8 is an element. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 3

R. 1 Example 2 Listing the Elements of a Set (page 3) Use set notation, and list all the elements of each set. (a) {x|x is a natural number between 8 and 12} {9, 10, 11} (b) {x|x is a natural number greater than 6 and less than 8} {7} Copyright © 2017, 2013, 2009 Pearson Education, Inc. 4

R. 1 Example 3 Examining Subset Relationships (page 4) Let U = {3, 9, 15, 21, 27, 33, 39}, A = {3, 9, 15, 21, 27, 33}, B = {3, 9, 21, 27}, C = {9, 27, 33}, and D = {3, 27}. Determine whether each statement is true or false. (a) false (b) true Copyright © 2017, 2013, 2009 Pearson Education, Inc. 5

R. 1 Example 3 Examining Subset Relationships (cont) Let U = {3, 9, 15, 21, 27, 33, 39}, A = {3, 9, 15, 21, 27, 33}, B = {3, 9, 21, 27}, C = {9, 27, 33}, and D = {3, 27}. Determine whether each statement is true or false. (c) false (d) true Copyright © 2017, 2013, 2009 Pearson Education, Inc. 6

R. 1 Example 4 Finding the Complement of a Set (page 4) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A= {2, 4, 6, 8}, B = {3, 6, 9} Find each set: a. A′ b. B′ c. U′ d, Ø′ a. A′ contains the elements of U that are not in A: {1, 3, 5, 7, 9} b. B′ contains the elements of U that are not in B: {1, 2, 4, 5, 7, 8} c. U′ = Ø Copyright © 2017, 2013, 2009 Pearson Education, Inc. d. Ø′ = U 7

R. 1 Example 5 Finding Intersections of Two Sets (page 5) Find the following. Identify any disjoint sets. a) {15, 20, 25, 30} ∩ {12, 18, 24, 30} = {30} The element 30 is the only one belonging to both sets. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 8

R. 1 Example 5 Finding Intersections of Two Sets (cont. ) Find the following. Identify any disjoint sets. (b) {3, 6, 9, 12, 15, 18} ∩ {6, 12, 18, 24} = {6, 12, 18} The elements 6, 12, and 18 belong to both sets. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 9

R. 1 Example 5 Finding Intersections of Two Sets (cont. ) Find the following. Identify any disjoint sets. (c) {6, 7, 8} ∩ {678} = no solution; disjoint sets Copyright © 2017, 2013, 2009 Pearson Education, Inc. 10

R. 1 Example 6 Finding Unions of Two Sets (page 5) Find the following. (a) {1, 3, 5, 7, 9} U {3, 6, 9, 12} List the elements of the first set, then include the elements from the second set that are not already listed. {1, 3, 5, 7, 9} U {3, 6, 9, 12} = {1, 3, 5, 6, 7, 9, 12} Copyright © 2017, 2013, 2009 Pearson Education, Inc. 11