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## Set Operations

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**Set Operations**Chapter 2 Sec 3**Union**• What does the word mean to you? • What does it mean in mathematics?**Definition**• The union of sets A and B, written , is the set of elements that are members of either A or B(or both). • Using set-builder notation, {x:x is a member of A or x is a member of B}.**The union of more than two sets is the set of all elements**belonging to at least one of the sets.**Example**• Find the union of the following pair of sets. • A={1,3,5,8,9} and B={2,4,6,7,8,}**Solution**• = {1,2,3,4,…,9} • The solution in the final answer we list the elements in order and did not list duplicate elements because doing so does not affect set equality.**Intersection**• The essential idea of intersection is a region that is common to both sets.**Definition**• The intersection of sets A and B, written , is the set of elements common to both A and B. • Using set-builder notation, ={x:x is a member of A and x is a member of B}.**The intersection of more than two sets is the set of**elements that belong to each of the sets. • If =, then we say that A and B are disjoint.**r3**Inside the 2 circles are shaded.**r3**Which region would be shaded?**Complement**• If A is a subset of the universal set U, the complement of A is the set of elements of U that are not elements of A. This set is denoted by A’. • Using set builder notation,**Venn diagram: Complement**r1 What would be the complement?**Example**• Find the complement of each set. • U ={1,2,3,…10} and A ={2,4,6,8} • A’ = {1,3,5,7,9} • U is the set of cards in a standard 52 card deck, and F is the set of face cards. • F’ is the set of nonface cards.**Set difference**• The difference of sets B and A is the set of elements that are in B but not in A. This set is denoted by B-A. • Using set builder notation, • B-A = {x:x is a member of B and x is not a member of A}.**Venn for set difference, B-A**B A r3 Which region would be shaded?**Examples of Set difference.**• Find the set difference. • Find {3, 6, 9, 12}-{x:x is an even integer} • Therefore we will remove all the even integers to get {3, 9}