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### 23 Cards in this Set

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