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dm-lec1-sets-p - Sets Sets and Logic Chapter 1(1.1 Sets...

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Sets and Logic Chapter 1 (1.1 Sets) September 2, 2009 Sets A set is a collection of objects, d i t t k i t t order is not taken into account. Objects = elements members Objects = elements, members How to describe it? By listing all members: A = {1 2 3 4} – By listing all members: A = {1,2,3,4} – By listing a property necessary for membership: B = {x | x is a positive, even integer} – Symbol: [email protected] 2 CS204 Discrete Math (Fall 2009) Sets Element C Cardinality If X is a finite set, we let |X| = number of elements in X • Example: what is the cardinality of the set {R,Z} =? Membership Membership Empty (or null or void) set, Two sets X and Y are equal: X=Y For every x, if x X, then x Y, and for every x, if x Y, then x X. Subset A B Subset A Proper subset A B Power set: set of all subsets (proper or not) of a set X [email protected] 3 CS204 Discrete Math (Fall 2009) Sets Power set If |X| | | 2 n If |X| = n, | | = 2 – Formal proof in Section 2.4 Set operations – Union Union – Intersection
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