week2 - Basic Set Theory A set is a collection of elements....

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week 2 1 Basic Set Theory •A set is a collection of elements. Use capital letters, A , B , C to denotes sets and small letters a 1 , a 2 , … to denote the elements of the set. • Notation: means the element a 1 is an element of the set A A = { a 1 , a 2 , a 3 }. • The null , or empty set , denoted by Ф , is the set consisting of no points. Thus, Ф is a sub set of every set. • The set S consisting of all elements under consideration is called the universal set . A a 1
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week 2 2 Relationship Between Sets • Any two sets A and B are equal if A and B has exactly the same elements. Notation: A=B . • Example: A = {2, 4, 6}, B = { n ; n is even and 2 n 6} A is a subset of B or A is contained in B , if every point in A is also in B . Notation: • Example: A = {2, 4, 6}, B = { n ; 2 n 6} = {2, 3, 4, 5, 6} B A
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week 2 3 Venn Diagram • Sets and relationship between sets can be described by using Venn diagram. • Example: We toss a fair die. What is the universal set S ? …
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week 2 4 Union and Intersection of sets • The union of two sets A and B , denoted by , is the set of all points that are in at least one of the sets, i.e., in A or B or both. Example 1: We toss a fair die… • The intersection of two sets A and B , denoted by or AB , is the set of all points that are members of both A and B . • Example 2: The intersection of A and B as defined in example 1 is … B A B A
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week 2 5 Properties of unions and intersections Unions and intersections are: • Commutative, i.e.,
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week2 - Basic Set Theory A set is a collection of elements....

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