14111cwir5ws.1

14111cwir5ws.1 - , denoted A c is the set of all elements...

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c ± Kendra Kilmer September 30, 2011 Fall 2011 Week-in-Review #5 courtesy: Kendra Kilmer (covering Sections 6.1, 6.2, and 6.3) Section 6.1 We can either use roster notation or set-builder notation to represent a set. Two sets A and B are equal , written A = B , if and only if they have exactly the same elements. If every element of a set A is also an element of a set B , then we say that A is a subset of B and write A B . If A and B are sets such that A B but A 6 = B , then we say A is a proper subset of B written A B The set that contains no elements is called the empty set and is denoted by /0. It is a subset of all sets. The universal set is the set of all elements of interest in a particular problem. We use Venn Diagrams to visually represent sets. The universal set U is represented by a rectangle and subsets of U are represented by circles inside of the rectangle. The union of A and B , written A B is the set of all elements that belong to A or B . The set of elements in common with the sets A and B , written A B , is called the intersection of A and B . The complement of A
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Unformatted text preview: , denoted A c is the set of all elements in U that are not in A . • Two sets A and B are disjoint if A ∩ B = /0. • De Morgan’s Laws: Let A and B be sets. Then ( A ∪ B ) c = A c ∩ B c and ( A ∩ B ) c = A c ∪ B c . 1. Let U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } , A = { 1 , 3 , 5 , 7 , 9 } , B = { 2 , 4 , 6 , 8 , 10 } , C = { 1 , 5 , 8 , 9 } , D = { 8 , 10 } . Find the following: (a) A ∪ C (b) B ∩ D (c) C c (d) A ∪ ( B ∩ D ) (e) C ∩ ( A ∪ D ) c 2. Using the following sets, determine whether each statement is True or False. U = { 1 , 2 , 3 , 4 , 5 , 9 , 12 , 15 , 18 } A = { 2 , 4 , 9 , 15 } , B = { 1 , 3 , 15 , 18 } , C = { 5 , 9 , 15 } (a) { 2 , 15 } ∈ A (b) ( B ∪ C ) c ∩ A c = /0 (c) A has 16 subsets (d) /0 ⊂ B (e) /0 ∪ C = { 5 , 9 , 15 } (f) A and B are disjoint sets. 3. List all subsets of the set A where A = { x | x is an integer between 3 and 5 inclusive } . 1...
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This note was uploaded on 03/04/2012 for the course MATH 141 taught by Professor Jillzarestky during the Fall '08 term at Texas A&M.

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