Discrete Structure lecture_5

Apr 28th, 2015
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It includes all the details about the Discrete structure with examples.Step by step solution.

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DISCREAT STRUCTURELECTURE # 5SET THEORYKHAWAJA TARIQ MAHMOODLecture # 5SET THEORYSET:A well defined collection of (distinct) objects is called a set.ELEMENTS:The objects are called the elements or members of the set.Sets are denoted by capital letters A, B, C , X, Y, Z.The elements of a set are represented by lower case letters a, b, c, , x, y, z.If an object x is a member of a set A we write x A , which reads x belongs to A orx is in A or x is an element of A, otherwise we write x A , which reads x does notbelong to A or x is not in A or x is not an element of A.REPRESENTATION OF SET:Sets are represented as follows.TABULAR FORM:Listing all the elements of a set, separated by commas and enclosed within braces orcurly brackets{}.EXAMPLE:In the following examples we write the sets in Tabular Form.A = {1, 2, 3, 4, 5}is the set of first five Natural Numbers.B = {2, 4, 6, 8, , 50} is the set of Even numbers up to 50.C = {1, 3, 5, 7, 9, } is the set of positive odd numbers.NOTE:The symbol is called an ellipsis. It is a short for and so forth.DESCRIPTIVE FORM:Stating in words the elements of a set.EXAMPLE:Khawaja Tariq Mahmood.Page 2Lecture # 5SET THEORYA = set of first five Natural Numbers.B = set of positive even integers less or equal to fifty.C = set of positive odd integers.SET BUILDER FORM:Writing in symbolic form the common charact

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