Copyright © 2014 Curt Hill Set Operations Now it gets fun

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


Union• A binary operation that takes two sets

and produces the set containing every element from both of the two sets

• AB is the notation• Union is associative and commutative• If A = {1,2,3,4,5}• If B = {2,4,6,8}• Then AB = {1,2,3,4,5,6,8}


Intersection• A binary operation that takes two sets

and produces the set containing only those elements that are in both sets

• Notation AB• Intersection is associative and

commutative.• If A = {1,2,3,4,5}• If B = {2,4,6,8}• Then AB = {2,4}


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}


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 (AB)-(AB)


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


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


Next• We will next consider Venn diagrams


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Copyright © 2014 Curt Hill Set Operations Now it gets fun