chapter2

# chapter2 - Chapter 2 Sets and Counting Definition The...

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Unformatted text preview: Chapter 2 Sets and Counting Definition. The branch of mathematics that deals with sets is called set theory . 2.1 Sets and Set Operations Definition. A set is a collection of objects. Definition. The objects in a set are called elements of the set. Definition. A well-defined set is a set in which we know for sure if an element belongs to that set. Example 1: a the set of all movies in which John Cazale appears. b the set of all the states in the USA. c the set of best TV shows of all time. 2.1.1 Notation A capital letter is usually used to denoted for a set. Definition. Roster notation (listing notation) is a method of describing a set by listing each element of the set. • Each distinct element is listed only once. • the order of the elements doesn’t matter. • The symbols { & } are called set braces . • The symbol ∈ stands for the phrase is an element of , and negationslash∈ stands for is not an element of . Definition. The cardinal number of a set A is the number of elements in the set and is denoted by n(A). Example 2: Let C be the set of all movies in which John Cazale appears. The Roster notation would be C= { The Godfather, The Conversation, The Godfather II, Dog Day Afternoon, The Deer Hunter } . 17 Example 3: Let set A be the set of odd numbers greater than zero, and less than 10. The roster notation of A = Example 4: Let set B be the set of letters in the word “time” The roster notation of B = Two sets are equal if they contain exactly the same elements. Example 5: Let M is the set of all letters in the word “item”; Let N is the set of all letters in the word ”time”. The roster notation of M = The roster notation of N = Example 6: The set Z is the set of all integer numbers. Definition. Self-builder notation lists the rules that determine whether an object is an element of the set rather than the actual elements. Example 7: Let D be a set of all whole numbers which is read as “the set of all x such that x is great than zero and x is an integer.” Example 8: V = { persons | the person is a registered voter in Detroit } which is read as “the set of all the person such that the person is a registered voter in Detroit.” In set-builder notation, the vertical line stands for the phrase “ such that ”. Whatever is on the left side of the line is the general type of things in the set, while the rules about set membership are listed on the right. Example 9: W = { women | the woman is a former U.S. president } Definition. A set that has no elements is called an empty set and denoted by ∅ or by {} . Example 9 ( cont. ): W = ∅ = {} 18 2.1.2 Universal Set and Subsets Definition. The Universal Set denoted by U is the set of all possible elements used in a problem....
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chapter2 - Chapter 2 Sets and Counting Definition The...

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