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23 Cards in this Set
- Front
- Back
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Set
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a collection of objects, which are called elements.
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3 Methods Used to Indicate Sets
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1) Description
2) Roster Form 3) Set-Builder Notation |
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Description of Sets
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-use words
-a simple sentence Ex: The set of blue items. The set of triangles |
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Roster Form
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-listing all elements in the set
-use braces { } Ex: {yellow triangle, blue triangle} |
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Set-Builder Notation
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-uses symbols
Ex: D= {x I x is a triangle} |
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Natural Numbers
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{1, 2, 3, 4, ...}
symbol: N |
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Whole Numbers
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{0, 1, 2, ,3, ...}
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Integers
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{..., -2, -1, 0, 1, 2, ...}
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Finite
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-has a stopping point
-"countable" |
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Infinite
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-never ending
-fractions |
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Equality of Sets
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Sets A and B are equal if they contain exactly the same elements.
Ex: A= {1, 2, 3} B= {3, 1, 2} A=B |
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Equivalent of Sets
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-Contain the same number of elements
Ex: A= {a, b, c} B= {d, e, f} |
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Cardinality
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-How many elements are in the set
-written as: n(A) Ex: A= {a, c, 1, 4, 5) n(A)=5 |
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Null or Empty Set
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-no elements in the set
-written as { } or ∅ |
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Universal Set
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-All elements in the context of the problem
-written as U |
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Subset
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A is a subset of B if and only if all elements of A are contained in B
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Proper Subset
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A is a proper subset of B if and only if A is a subset of B AND A does not equal B.
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{}
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is a subset of every set and a proper subset
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Number of Subsets
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2 , where n is the number of elements in the set
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Complement
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A all elements not in A
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Union
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A B
or |
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Intersection
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A B
and |
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Number of Proper subsets
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2 -1
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