Copyright © 2014 Curt Hill Set Operations Now it gets fun.

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Presentation transcript:

Copyright © 2014 Curt Hill Set Operations Now it gets fun

Set Operations Operations, either unary or binary that operate on sets and produce sets. Basic operations include union, intersection, and complementation. From these other operations can be built, the most common of which is set difference Copyright © 2014 Curt Hill

Union A binary operation that takes two sets and produces the set containing every element from both of the two sets A  B is the notation Union is associative and commutative If A = {1,2,3,4,5} If B = {2,4,6,8} Then A  B = {1,2,3,4,5,6,8} Copyright © 2014 Curt Hill

Intersection A binary operation that takes two sets and produces the set containing only those elements that are in both sets Notation A  B Intersection is associative and commutative. If A = {1,2,3,4,5} If B = {2,4,6,8} Then A  B = {2,4} Copyright © 2014 Curt Hill

Set Difference A binary operation that takes two sets and produces a set, denoted by A-B The resulting set contains every element in A that is not an element in B If A = {1,2,3,4,5} If B = {2,4,6,8} Then A-B = {1,3,5} B-A = {6,8} Copyright © 2014 Curt Hill

Symmetric Difference The union of the two set differences If A = {1,2,3,4,5} If B = {2,4,6,8} Then A ⨁ B is {1,3,5,6,8} This is the same as (A  B)-(A  B) Copyright © 2014 Curt Hill

Complementation A unary operation that takes a set and produces the set containing the universe of discourse with every element from the original removed Symbol is the set with over bar: Ā. The same as U-A Copyright © 2014 Curt Hill

Sets and Logic Union corresponds to Or Intersection corresponds to And Complementation corresponds to Negation Subset corresponds to Implication –Mutual subset corresponds to biconditional or equivalence Copyright © 2014 Curt Hill

Next We will next consider Venn diagrams Copyright © 2014 Curt Hill