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02 - Lecture 2 Sets Relations and Functions(a Review Sets A...

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Lecture 2: Sets, Relations, and Functions (a Review) Sets A set is a collection of objects. Example: L = { a, b, c, d } is a set of four elements . a L denotes a is in L , and z L denotes z is not in L . The empty set , denoted by , contains no elements. A set is finite if it has a finite number of elements. Otherwise, the set is infinite . A is a subset of B , denoted A B , if every element in A is an element in B . Two sets A and B are equal ( A = B ) if A B and B A . A B means A is a proper subset of B (i.e., A = B ). By this definition, is a proper subset of any non-empty set. 1

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Sets Set operations. Let A and B be sets. Intersection : A B = { x : x A and x B } . If A B = , we say that A and B are disjoint . Union : A B = { x : x A or x B } . Difference : A B = { x : x A and x B } . Power sets and partition. The set of all subsets of a set A , denoted by 2 A , is called the power set of A . For example, 2 { c,d } = {∅ , { c } , { d } , { c, d }} .
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