0
Presumed Knowledge
3
Example
This can be expressed as the set
This means the set of numbers
x
, where
x
is greater than or equal to 1,
where
x
is a member of the real numbers.
5
x
:
x
1,
x
H
6
.
4
5
2
3
1
0
1
Example
Draw
and
on a Venn diagram and write down
the intersection and union of
P
and
Q
. State why
P
is a subset of
Q
.
and
Here all of set
P
is contained in set
Q
and so
P
is a subset of
Q
, that is,
P
(
Q
.
P
´
Q
5
2, 3, 5, 7
6
.
P
¨
Q
5
3, 5
6
Q
5
2, 3, 5, 7
6
P
5
3, 5
6
Q
P
2
7
5
3
It is important to be able to express an inequality as a set.
1
Express each inequality as a set.
a
b
c
d
2
For the sets given, draw a Venn diagram and state the intersection and
union of the sets.
a
b
c
d
e
3
If
and
state the set
A
.
Draw a Venn diagram of these two sets.
A
¨
B
5
7, 9, 11
6
,
B
5
3, 7, 9, 11, 13
6
,
A
(
B
P
5
5, 1, 2
6
,
Q
5
5, 1, 2, 7, 11
6
K
b
1
2
,
3
4
, 9
r
,
L
b
1
2
, 9, 11, 17
r
F
5
3,
2, 10
6
,
G
5
1, 2, 7
6
C
5
0, 3, 7
6
,
D
5
3, 9, 11, 13
6
A
5
1, 2, 3
6
,
B
5
3, 4, 5
6
Exercise
1
2
3
1
0
1
2
3
2
3
4
1
0
1
2
2
3
4
1
0
1
2
2
3
1
0
1
2
0
Presumed Knowledge
2
Example
Draw
and
on a Venn diagram and write down
the intersection and union of
A
and
B
.
The sets
A
and
B
overlap as an intersection exists. The intersection is
The union of the sets is
A
´
B
5
1, 2, 5, 7, 9
6
.
A
¨
B
5
2, 5
6
.
B
5
2, 5, 7, 9
6
A
5
1, 2, 5
6
Example
Draw
and
on a Venn diagram and write
down the intersection and union of
C
and
D
.
Here the sets do not overlap so
C
´
D
5
2, 3, 7, 11, 13, 19
6
C
¨
˛˛
D
.
D
5
2, 3, 13
6
C
5
7, 11, 19
6
A
B
7
2
1
5
9
C
D
19
7
11
13
2
3
denotes the union of two sets. Union means all the members that are in either
set. This is analogous to “or”.
or
means “is a subset of”. This is analogous to
and
for numbers.
6
(
´
Example
What does
mean?