Examples:
1.
R
from
{
1
,
2
,
3
,
4
,
5
}
to
{
1
,
2
,
3
,
4
,
5
}
(
R
on
{
1
,
2
,
3
,
4
,
5
}
)
where
R
=
{
(1
,
1)
,
(1
,
2)
,
(1
,
3)
,
(3
,
4)
,
(2
,
4)
,
(4
,
5)
,
(5
,
4)
}
.
2.
LE
from
R
to
R
(
LE
on
R
)
where
x LE y
⇔
x
≤
y
LE
=
{
(
x, y
)
∈
R
2

x
≤
y
}
3.
P
from
Z
to
Z
(
P
on
Z
) where
x P y
⇔
x
and
y
are both even or both
odd
P
=
{
(
x, y
)
∈
Z
2

x
and
y
are both even or both odd
}
4.
T
from
P
(
{
a, b, c
}
) to
Z
where
A T x
⇔ 
A
 ≥
x
{
1
}
T
0
(
∅
,
2)
/
∈
T
5. All functions are binary relations but not all binary relations are func
tions. For example, the binary relations above are not functions.
6.
B
on
R
3
where
(
x, y, z
)
∈
B
⇔
y < x < z
or
z < x < y
7. relational databases
Let
A
1
= the set of all possible student names
A
2
= the set of all possible student numbers
A
3
= the set of all possible courses
A
4
=
{
A+, A, A, B+, B, B, C+, C, C, D+,
D, F
}
Define
R
on
A
1
×
A
2
×
A
3
×
A
4
as follows: (
w, x, y, z
)
∈
R
⇔
the student
with name
w
and student number
x
took course
y
and received a grade
of
z
in that course.
2