Download 2.1 - Set Concepts.notebook

2.1 ­ Set Concepts.notebook
August 27, 2015
2.1 ­ Set Concepts
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2.1 ­ Set Concepts.notebook
August 27, 2015
TERMINOLOGY
Set:
A collection of objects
Elements (members):
Well Defined Set:
Set Description:
Braces:
i.e.: The united States is a set of 50 states, and Illinois is a member of the set of states.
An object in a set
The contents of the set can be clearly determined.
A method of describing a set by using a sentence.
{ } ­ used to list a set of elements, everything within the {} is an element of the set
Roster Form:
A method of describing a set by listing the specific elements.
Natural Numbers: 1, 2, 3, 4, 5, ...
Set­Builder Notation:
Finite Set:
Infinite Set:
A method of describing a set using symbols
A set that either contains no elements or the number of elements in the set is a natural number.
A set that is not finite
One­to­one Correspondence:
Every element in Set A can be matched with exactly one element of Set B and every element of Set B can be matched exactly with one element of Set A
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2.1 ­ Set Concepts.notebook
August 27, 2015
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2.1 ­ Set Concepts.notebook
August 27, 2015
KEY CONCEPTS
Set A is equal to set B, symbolized by A = B, iff set A and set B contain exactly the same elements
The cardinal number of a set A, symbolized by n(A), is the number of elements in set A.
Set A is equivalent to set B iff n(A) = n(B).
If two sets are equal, then they are equivalent.
If two sets are equivalent, then they may or may not be equal.
The set that contains no elements is called the empty set or null set and is symbolized by { } or ∅.
A universal set, symbolized by U, is a set that contains all the elements for any specific discussion.
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2.1 ­ Set Concepts.notebook
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2.1 ­ Set Concepts.notebook
August 27, 2015
Example 1: Write a description of the set containing the elements Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
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2.1 ­ Set Concepts.notebook
August 27, 2015
Example 2: Express the following in roster form.
a) Set A is the set of natural numbers less than 6
b) Set B is the set of natural numbers less than or equal to 50.
c) Set P is the set of planets in Earth's solar system.
d) Set X is the set of natural numbers between 5 and 8.
e) Set R is the set of natural numbers between 5 and 8, inclusive.
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2.1 ­ Set Concepts.notebook
August 27, 2015
Example 4: Use set builder notation to describe the following sets.
A) A = {1, 2, 3, 4, 5, 6}
B) Set A is the set of all fruit whose name starts with the letter A.
C) C = {North America, South America, Europe, Asia, Australia, Africa, Antarctica}
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2.1 ­ Set Concepts.notebook
August 27, 2015
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2.1 ­ Set Concepts.notebook
August 27, 2015
Example 6: Write the following in roster form.
A = {x | x ∈ N and 2 < x < 8}
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2.1 ­ Set Concepts.notebook
August 27, 2015
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