Math M118 Finite Math PP Chapter 2.pdf - Math M118 Finite...

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Math M118 Finite MathChapter 2, Set TheoryBy: Annemarie Schreiber
Section 2.1Sets and SubsetsAsetis awell-definedcollection of objects that are calledelementsormembers.Acapital letter is used to name the set.Well defined? Are the following groupings sets?
Example:Let?represent the set of all US states starting with the letter A. Arethe states of Alabama or Indiana elements of??.∉ ?
Ways to represent setsRoster method:A listing of all the elements that belong to the set. The elements are listed betweena pair of braces and elements are separated by a comma.Use the roster method for the set in of the days of the week.𝑊 = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}Ex.Use the roster method to list all the elements in set?(states with an A)
Ex.Use the roster method to list all elements of the set of letters in thealphabet, call the set?.
Set Builder Notation:The set builder notation explains the property of the elements in a set?as follows? = {?|? satisfies this property}.We read:?is the set of all elements?, such that?satisfies thispropertyEx.Use the set builder method for the set𝑊.𝑊 =?|?is a day of the week(read: SetWis the set of all elementsxsuch thatxis a day of the week)Ex.Use the set builder notation to write sets?, ?
Ex.List all the elements of the setWthat begin with the letter E.
Ex.Fill in the appropriate sign:21,2,3,461,2,3,4The set with no elements is represented by:
Cardinality of a SetCardinality:The number of distinct elements in a set is called thecardinalnumberand is represented by?(?).Ex.Find the cardinal number of the following sets:? =2,4,6,8?(?) =? = {0}?(?) =? = { }?(?) =? = {?, ?, ?, ?, … ?}?(?) =Ex.What is the cardinal number ofV, the set of vowels from thealphabet?
SubsetsSubset:If every element in set A is also an element in set B the set A isasubsetof set B.⊂, ⊄stands for “is a subset of”,stands for “is not a subset of.”Every set is a subset of itself:? ⊆ ?The empty set is subset of every set:{ } ⊆ ?Equality:Two sets areequalif and only if every element in the first setis exactly the same as every element in the second set.? ⊆ ? and ? ⊆ ? if and only if ? = ?

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