Download 2.1 - Kean University

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SEVENTH EDITION and EXPANDED SEVENTH EDITION
Slide 2-1
Chapter 2
Sets
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2.1
Set Concepts
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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 .
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Well-defined Set
„
„
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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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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.
(The Natural Numbers are the counting numbers :
1,2,3,4,5…)
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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}.
„
Read this as “the set of all x such that x is an even
number and less than or equal to 10”; the vertical bar in
the set builder notation is read as “such that”
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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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Infinite Set
„
„
An infinite set contains an indefinite 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 2-9
Equal Sets
„
„
Equal sets have the exact same elements in
them, regardless of their order.
Symbol:
A=B
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Cardinal Number
„
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The number of elements in a finite set A is its
cardinal number.
Symbol: n(A)
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Equivalent Sets
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Equivalent sets have the same number of
elements in them.
Symbol: n(A) = n(B)
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Empty (or Null) Set
„
„
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A null (or empty set ) contains absolutely NO
elements.
{ }
Symbol: ∅ or
Use just one of these symbols for the empty
set.
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Slide 2-13
Universal Set
„
The universal set contains all of the possible
elements which could be discussed in a
particular problem.
Symbol: U
For example, if a problem is talking only about
students at Kean University, then the Universal set
U is “Kean University Students”
„
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Next Steps
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Study Examples 1-7 in the textbook
Homework from the textbook for this section:
19-24, all; 35-57, odds
Do the online homework for this section
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