Sets
 Basic properties of sets       Two characteristics of a set    There are no repeated occurrences of elements  There is no particular order or arrangement of the elements     How do you show A is a subset of B?  If A and B are sets and every element of A is also an element of B, then A is a subset of B.   How do you show A = B?  A is a subset of B, and B is a subset of A   Operations on sets    Union - A union B = set of x s.t. x is an element of A or x is an element of B  Intersection - A intersect B = set of x s.t. x is an element of A and x is an element of B   Complement    Cardinality   Inclusion-Exclusion principle   | A ∪ B | = | A | + | B | − | A ∩ B |.     Inclusion-Exclusion for 3 sets   | A ∪ B ∪ C | = | A | + | B | + | C | − | B ∩ C | − | A ∩ B | − | A ∩ C | + | A ∩ B ∩ C |   Difference rule   | A − B | = | A | − | A ∩ B |.        


 
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