Game Development Reference
In-Depth Information
If you want to designate that a number
a
is less than 17 and is also an element of
set
A
, then you can use a logical ''and'' symbol
ð^Þ
:
fa j a
<
17
^ a j a 2 Ag
This expression reads, ''
a
such that
a
is less than 17
and a
such that
a
is an element
of set
A
.''
Unions and Intersections
Consider sets
A
and
C
:
A ¼f
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
g
C ¼f
1, 2, 3, 5, 7, 10, 11, 12, 14, 17
g
You can find some of the elements of set
C
in set
A
and some of the elements of
set
A
in set
C
. In other words, between sets
A
and
C
exists a group of elements that
are common to both sets. When you have a set of elements that are common to
both sets, you find the
intersection
of the two sets. To indicate the intersection of
two sets, you employ the
\
symbol:
A \ C
More explicitly, you indicate the members of the set using an equation:
A \ C ¼f
2, 3, 5, 7, 11, 17
g
Not all of the elements in set
C
are in set
A
, and not all of the elements in set
A
are
in set
C
. When you combine the elements of the two sets so that you have the
elements of both sets without duplicates, you create the union of the two sets. To
indicate the union of two sets, you employ the
[
symbol:
A [ C
To show the union explicitly, you use the same approach you use when showing
an intersection explicitly:
A [ C ¼f
1, 2, 3, 5, 7, 10, 11, 12, 13, 14, 17, 19, 23, 29, 31, 37, 41, 43, 47
g
