Operations on Sets

Recall that a set is a collection of elements.

Given sets A and B , we can define the following operations:

Operation
Notation
Meaning
Intersection
AB
all elements which are in both A and B
Union
AB
all elements which are in either A or B (or both)
Difference
AB
all elements which are in A but not in B
Complement
A ¯ (or A C )
all elements which are not in A

 

Example 1:

Let A={ 1,2,3,4 } and let B={ 3,4,5,6 } .

Then:

AB={ 3,4 }

AB={ 1,2,3,4,5,6 }

AB={ 1,2 }

A C ={ all real numbers except 1,2,3 and 4 }

Example 2:

Let A={ y,z } and let B={ x,y,z } .

Then:

AB={ y,z } AB={ x,y,z } AB= A C ={ everything except y and z }