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Unformatted text preview: Slide 2  1 Slide 2  1 Chapter 2 Sets Slide 2  2 Slide 2  2 2.1 Set Concepts Slide 2  3 Set A collection of objects, which are called elements or members of the set. Listing the elements of a set inside a pair of braces , { }, is called roster form . The symbol , read “is an element of,” is used to indicate membership in a set. The symbol , means “is not an element of.” ∈ ∈ Slide 2  4 Welldefined Set A set which has no question about what elements should be included. Its elements can be clearly determined. No opinion is associated with the members. Slide 2  5 Roster Form This is the form of the set where the elements are all listed, each separated by commas. Example: Set N is the set of all natural numbers less than or equal to 25. Solution: N = {1, 2, 3, 4, 5,…, 25} The 25 after the ellipsis indicates that the elements continue up to and including the number 25. Slide 2  6 Write the following in Roster Form a. The set of states whose name begins with the letter C C = {California, Colorado, Connecticut} b. The set of natural numbers less than 10 N = {1, 2, 3, 4, 5, 6, 7, 8, 9} c. The set of Heisman Trophy winners from the University of Florida F = {Spurrier, Tebow, Weurffel} Slide 2  7 D = { X l condition(s) } Set is the all such that the condition(s) x nust meet Name set of elements in order to be a member of (D) X the set. Set Builder Notation Slide 2  8 SetBuilder (or SetGenerator) Notation A formal statement that describes the members of a set is written between the braces. A variable may represent any one of the members of the set. Example: Write set B = {2, 4, 6, 8, 10} in set builder notation. Solution: B = x x ∈ N and x is an even number ≤ 10 { } . Slide 2  9 SET BUILDER EXAMPLE A = { x l x N and x > 12}, we would read this as A is the set of all elements x such that x is a Natural number and x is greater than 12. G = { x l x is a vowel}, we would read this as G is the set of vowels of the alphabet. ∈ Slide 2  10 Write in set Builder Notation B = {4, 5, 6, 7, 8, 9, 10} B = { x l x N and 3 < x < 11} C = {3, 6, 9, 12 ……} C = { x l x N and x is a multiple of 3} A is a set of holidays in the United States in September A = { x l x is labor day} ∈ ∈ Slide 2  11 Set Builder Notation to Roster Form B = { x l x N and x is even} B = {2, 4, 6, 8, 10 ……..} ∈ Slide 2  12 Finite Set A set that contains no elements or the number of elements in the set is a natural number. Example: Set S = {2, 3, 4, 5, 6, 7} is a finite set because the number of elements in the set is 6, and 6 is a natural number. Slide 2  13 Infinite Set An infinite set contains an indefinite (uncountable) number of elements....
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This note was uploaded on 12/12/2011 for the course MGF 1106 taught by Professor Holbrook during the Spring '10 term at Santa Fe College.
 Spring '10
 HOLBROOK

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