Section 1.1 Sets and the Real Numbers 3 Symbol Meaning Example Verbal Statement Union A B = 5 3, 4, 5, 6, 76 “A union B” The union is the set of elements that are in A or in B or in both. Elements do not need to be repeated if they are in both sets. Intersection A B = 5 3, 4, 56 “A intersect B” The intersection is the set of elements that are in both A and B. Objective 1 Examples Determine the requested information for the given sets. 1a. Use the roster method to write the set A = 5xux is a positive even number6 in another way. Solution 1a. The roster method lists the numbers in the set explicitly. So, the set A = 52, 4, 6, 8, 10, . . .6 . 1b. Let A = 53, 6, 9, 12, 156 and B = 56, 12, 18, 246. Find A B and A B. Solution 1b. The set A B means to join all elements of A and all elements of B into one set. Therefore, if A = 53, 6, 9, 12, 156 and B = 56, 12, 18, 246 , then A B = 53, 6, 9, 12, 15, 18, 246 The set A B means to find the elements that are in both A and B. Therefore, A B = 56, 126 1c. The following table provides information about each continent. (Source: www.worldatlas.com) Continent Population in 2009 Land Mass Africa 1,000,050,000 30,065,000 km2 Antarctica 0 13,209,000 km2 Asia 3,879,000,000 44,579,000 km2 Australia/Oceania 32,000,000 8,112,000 km2 Europe 731,000,000 9,938,000 km2 North America 528,720,588 24,474,000 km2 South America 379,500,000 17,819,000 km2 Let A = 5x|x is a continent with a population less than 50 million6 and B = 5x|x is a continent with land mass greater than 20 million km26. i. State set A using the roster method. ii. State set B using the roster method. iii. Is Asia A B? Solution 1c. i. To be a member of set A, the continent must have a population less than 50 million. So, A = 5Antarctica, Australia/Oceania6 . ii. To be a member of set B, the continent must have a land mass greater than 20 million km2. So, B = 5Africa, Asia, North America6. iii. A B is the set of elements that are members of both A and B. There are no continents listed in both sets, so A B = . Therefore, Asia ∉ A B.
hendricks_intermediate_algebra_1e_ch1_3
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