1.1 sets, set operations and number sets
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Sets (College Algebra)TRANSCRIPT
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CHAPTER 1ALGEBRA AS THE STUDY OF STRUCTURESMATH 17College Algebra and Trigonometry
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Chapter Outline1.Sets, Set Operations and Number Sets2.The Real Number System3.The Complex Number System4.The Ring of Polynomials5.The Field of Algebraic Expressions6.Equations7.Inequalities
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Chapter 1.1Sets, Set Operations, and Number Sets
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ObjectivesAt the end of the section, we should be able to:
1.Identify special number sets2.Perform set operations on number sets3.Draw Venn diagrams4.Identify finite and infinite sets of numbers and how to represent them
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Set and Set NotationsA set is a well-defined collection of objects.
It should be possible to determine (in some manner) whether an object belongs to the given collection or not.
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Example 1.1.1Which of the following collection of objects are sets?
The collection of all:1.colleges in UPLB.SET2.counting numbers from 1 to 100SET3.provinces near Laguna.NOT A SET
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4.planets in the solar system.SET5.pretty instructors in UPLB.NOT A SET6.letters in the word algebra.SET7.points in a line.SET8.MATH 17-A students who can fly.SET
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ElementIf an object belongs to the set, it is called an element of the set.
Otherwise, the object is not an element of the set.
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Example 1.1.2
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Equal Sets
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Example 1.1.3
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Example 1.1.4
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Finite/Infinite Sets
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Example 1.1.5Determine if the following sets are finite or infinite.
1.Set of counting numbers from 1 to 5FINITE
2.Set of all professors in UPLB.FINITE
3.Set of points in a circle.INFINITE
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4.Set of counting numbers between 1 and1,000,000,000FINITE
5.Set of grains of sand in a beachFINITE
6.Set of counting numbers greater than 1INFINITE
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Describing Sets
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Describing Sets
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Example 1.1.6
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Example 1.1.7
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Example 1.1.8
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Example 1.1.9
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One-to-one Correspondence
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Example 1.1.10
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Example 1.1.11Is there a one-to-one correspondence between
the set of days in a week and
the set of months in a year.
NO
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Example 1.1.12Let A = { 1, 2, 3, 4 }B = { 3, 6, 9, 12 }C = { -4, -3, -2, -1, 1, 2, 3, 4 }
Is there a one-to-one correspondence between set A and set B? YES
Is there a one-to-one correspondence between set A and set C? NO
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Example 1.1.13
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Equivalent Sets
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Example 1.1.14
True or False
1.Equal sets are equivalent.
2.Equivalent sets are equal.
3.If set A is equivalent to set B and set B is equivalent to set C, then A is equivalent to C.
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Subsets
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Subsets
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Example 1.1.15
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Subsets
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Subsets
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Equal Sets (Alternative Definition)
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Proper Subsets
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Example 1.1.16
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Empty Sets
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Example 1.1.17
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Empty Sets
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Venn Diagram
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Example 1.1.18
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Example 1.1.18
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Disjoint Sets
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Disjoint Sets
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Universal Set
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Example 1.1.19
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Complement
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ComplementExample 1.1.20
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Complement
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Complement
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Cardinality
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CardinalityExample 1.1.21
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Power SetExample 1.1.22
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Example 1.1.22
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Union
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Union
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Example 1.1.23
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Intersection
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Intersection
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Example 1.1.24
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Example 1.1.24
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Alternative Definition
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n(A U B)
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Example 1.1.25
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Example 1.1.26
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Example 1.1.26
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Example 1.1.26
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Example 1.1.26
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Example 1.1.26
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Example 1.1.26
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Example 1.1.27
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Cross Product
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Example 1.1.28
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Number Sets
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Number Sets
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Number Sets
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Number Sets
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Example 1.1.29
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End of Chapter 1.1
How to say that sets are not equal.******Larger sets - Subsets*******************************