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ch02MGF1106 - Chapter 2 Sets Slide Slide 2 1 2.1 Set...

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Slide 2 - 1 Chapter 2 Sets
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Slide 2 - 2 2.1 Set Concepts
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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.”
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Slide 2 - 4 Well-defined 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.
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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.
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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}
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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
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Slide 2 - 8 Set-Builder (or Set-Generator) 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 { } .
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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.
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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}
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Slide 2 - 11 Set Builder Notation to Roster Form B = { x l x N and x is even} B = {2, 4, 6, 8, 10 ……..}
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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.
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Slide 2 - 13 Infinite Set An infinite set contains an indefinite (uncountable) number of elements. The set of natural numbers is an example of an infinite set because it continues to increase forever without stopping, making it impossible to count its members.
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Slide 2 - 14 Equal sets have the exact same elements in them, regardless of their order.
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