Download SETS AND VENN DIAGRAMS A set is a group of

SETS AND VENN DIAGRAMS
A set is a group of objects. Each object in the set is called a member or element of that
set. A set is identified by a capital letter and braces { } to list the members of the set.
Set A = {1, 2, 3, 4}
This says that Set A has the members 1, 2, 3, and 4
A set with no members is called the empty set or null set. It is represented by empty
brackets { } or by the symbol Ø. For example, the set of even integers between 6 and 8
would be the empty set.
A finite set is a set in which the members can be listed or counted and the counting ends,
Set A above is finite. A list of the members in a set is called the roster. Finite sets can be
listed by roster, identified by description (rule), or illustrated by graphing on a number line.
Example:
Roster:
E = {2, 4, 6}
Description: E = {even integers between 0 and 8}
Number Line:
-2
-3
-1
0
1
2
3
4
5
6
7
An infinite set is a never-ending set. Examples of infinite sets are:
The set of whole numbers W = {0, 1, 2, 3, …}
The set of integers I = {…-2, -1, 0, 1, 2, …}
In these two examples, the sets can start to be listed, but the … indicates that the list
never ends. To represent integers on a number line, use dots, but also color in the arrows
at either end.
Example:
Graph the set of integers greater than 2
-3
-2
-1
0
1
2
3
4
5
6
7
Another type of infinite set is the set of real numbers, = {real numbers}. The set of real
numbers never ends and cannot be listed, but it can be described and shown on a number
line.
Example:
Graph {real numbers between 2 and 6}
-3
-2
-1
0
1
2
3
4
5
6
7
Special symbols are used in set notation. For example, using set A = {1, 2, 3, 4} we can
say that the number 1 is a member or element of set A by writing:
1∈ A
The following symbols are commonly used:
∈
∉
⊂
∪
∩
-
is an element of (member of)
is not an element of
is a subset of
union
intersection
To show that the set of {1, 2} is a subset of A, we would write: {1, 2} ⊂ A
Equal sets have exactly the same members. Equivalent sets have the same number of
elements (one to one correspondence), even though they may be different elements.
Example:
The sets {a, b} and {1, 2} are equivalent but not equal.
The union of sets is a new set containing all the members of the original sets. The
intersection of sets is a new set containing only those members which are common to all
the original sets.
Example:
B = {white, blue, green}
C = {white, yellow, orange}
D = {yellow, orange, blue, white}
G = {black, green}
D ∩ B = _______________________
D ∪ B = _______________________
B ∩ C ∩ D = _______________________
A subset is a set that is fully contained in another set. In the example above, C is a
subset of D, or C ⊂ D. Note that the empty set, Ø, is a subset of every other set.
Sets that have no members in common are called disjoint sets. Sets C and G above are
disjoint. Therefore, C ∩ G is the empty set (no members in common).
Grouping symbols can be used to show which operations to do first.
Venn Diagrams are another way to show the relationships between sets.
Example: For the figure below, find the following: 1.) X
Y = ________________
2.) X
W = _______________
3.) W
Y = _______________
4.) Z
X = _______________
5.) X
Y = ________________
3
W
8
5
2
Y
1
6
7
4
X
9 Z
6.) W
Y = _________________
7.) Z ⊂ ____
8.) Name two disjoint sets: _________
Example:
M = {real numbers between -2 and 4}
P = {positive real numbers}
For the sets M and P, GRAPH the following:
1.) Set M
2.) Set P
3.) M ∩ P
4.) M ∪ P
-3
-2
-1
0
1
2
3
4
5
6
7
-3
-2
-1
0
1
2
3
4
5
6
7
-3
-2
-1
0
1
2
3
4
5
6
7
-3
-2
-1
0
1
2
3
4
5
6
7