The union of two sets, denoted
*A*∪*B*
("
*A*
union
*B*
"), is the set of all members contained in either
*A*
or
*B*
or both. We can think of the union of two sets as the entire Venn diagram:

Union of Sets

In our first example,
*A*∪*B* = {0, 1, 2, 3, 4, 5, 6}
:

Union of
{1, 2, 3, 4, 5, 6}
and
{0, 2, 4, 6}

Union of
*A*
and
*B*

The easiest way to write the union of two sets is to write all the members in the first set, and then write all the members in the second set that haven't been written yet:

The number of members in
*A*∪*B*
should be **the total number of members in
A
plus the total number of members in
B
minus the number of members which are in both sets**. In example 3, X contains
5
members, Y contains
5
members, and there are
3
members which are in both X and Y. Thus,

The intersection of two sets, denoted
*A*∩*B*
("
*A*
intersect
*B*
") is the set of all members contained in *both*
*A*
and
*B*
. We can think of the intersection of two sets as the overlap in the Venn diagram:

Intersection of Sets

In our first example,
*A*∩*B* = {2, 4, 6}
:

Intersection of
{1, 2, 3, 4, 5, 6}
and
{0, 2, 4, 6}

Intersection of
*A*
and
*B*

Since

Take a Study Break!