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
all elements which are in both A and B
Union
all elements which are in either A or B (or both)
Difference
all elements which are in A but not in B
Complement
(or )
all elements which are not in A

 

Example 1:

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

Then:

= {3, 4}

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

= {1, 2}

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

Example 2:

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

Then:

= {y, z}

= {x, y, z}

=

= {everything except y and z}