# T2.2 - Sets are mathematical entities subject to certain...

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Sets are mathematical entities subject to certain operations. Set operations include union, intersection, difference and complement . Set operations are defined using logical notation to make them precise. Let A and B be sets in a universe U. Then: A B={x| x A \/ x B} “Union of A and B” A B={x| x A /\ x B} “Intersection of A and B” A-B={x| x A /\ x B} “Difference of A minus’ B” _ A = {x| x A} “Complement of A,” which may also be denoted A'. Note that A'=U-A. 1

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E.g. Let A={1,2,3,a} and let B={a,b,c,1} and let U={0,1,2,3,4,a,b,c,d,e} A B = {1,2,3,a,b,c} A B = {1,a} A-B={2,3} B-A={b,c} A'={0,4,b,c,d,e} B'={0,2,3,4,d,e} 2
If two sets have no elements in common they are said to be disjoint . Their intersection is . Formally: A and B are disjoint iff A B= There are numerous relationships among sets. Many of them are given in Table 1, p 124 (p. 89, ed. 5). They all involve showing that two sets are equal. This may be done by:

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## This note was uploaded on 02/09/2009 for the course CSC 226 taught by Professor Watkins during the Spring '08 term at N.C. State.

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T2.2 - Sets are mathematical entities subject to certain...

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