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Set Operations Chapter 2 Sec 3
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Union What does the word mean to you? What does it mean in mathematics?
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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}.
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The union of more than two sets is the set of all elements belonging to at least one of the sets.
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Example Find the union of the following pair of sets. ◦ A={1,3,5,8,9} and B={2,4,6,7,8,}
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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.
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Intersection The essential idea of intersection is a region that is common to both sets.
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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}.
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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.
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To help us understand we will use the Venn Diagram r2 r4 r1r1 r3r3
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r2r4 Inside the 2 circles are shaded. r3r3
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r2 r4 r3r3 Which region would be shaded?
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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,
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Venn diagram: Complement r2 r1r1 What would be the complement?
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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.
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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}.
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Venn for set difference, B-A r2 r4 r3r3 A B Which region would be shaded?
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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}
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